ACADEMIA COLOMBIANA DE CIENCIAS EXACTAS, FÍSICAS Y NATURALES

ACADEMIA COLOMBIANA DE CIENCIAS EXACTAS, FÍSICAS Y NATURALES

Miembro del Colegio Máximo de las Academias de Colombia

ALFONSO CASTRO

Profesión: Matemático

 Área (s) de especialización: Ecuaciones diferenciales

Categoría en la Academia Colombiana de Ciencias Exactas, Físicas y Naturales

Miembro Correspondiente X

Miembro de Número: dar número de silla

Miembro Honorario

Amigo de la Academia

Fecha de posesión, Miembro Correspondiente: 24 junio 1996

Fecha de posesión, Miembro de Número:

Fecha de posesión, Miembro Honorario:

Fecha de posesión, Amigo de la Academia

 

Datos personales

Fecha de nacimiento: día/mes/año

Lugar de nacimiento

Ciudad:

Departamento/Estado/Provincia:

País:

Dirección institucional:

Department of Mathematics

Harvey Mudd College

Claremont, CA 91711

Teléfonos. Código país, código ciudad, numero

Dirección electrónica (e-mail): e-mail: castro@g.hmc.edu

 

Hoja de vida (Curriculum Vitae en línea):

 

Página (sitio) web:

 

Títulos académicos:

Título, institución, año: Mathematics B.S. National University of Colombia, 1972

Título, institución, año: Mathematics M.S.    National University of Colombia , 1974

Título, institución, año: Mathematics Ph.D. University of Cincinnati, 1977

 Áreas de investigación

 

Reseña Biográfica (Extensa)

PROFESSIONAL EXPERIENCE:

  1. i) From June 2003 to date, Professor of Mathematics at Harvey Mudd College. From July 2008 to June 2009, Director of the Mathematics Clinic Program at Harvey Mudd College. From July 2004 to June 2008, Chair of the Department of Mathematics at Harvey Mudd College.
  2. ii) Cátedra de Excelencia, Universidad Complutense de Madrid, February 2017 to August 2017.

iii) University of Texas at San Antonio: From August 1998 to June 2003, Professor of Mathematics; from August 1998 to August 1999, Director of the Division of Mathematics, from September 2002 to June 2003, Chair of the Department of Applied Mathematics.

  1. iv) From September 1990 to August 1998, Professor of Mathematics at the University of North Texas.
  2. v) From September 1989 to August 1991, Program Director of Applied Mathematics and Classical Analysis (1990-91) at the National Science Foundation.
  3. vi) From September 1985 to August 1990, Associate Professor at the University of North Texas.

vii) From Sept. 1982 to August 1985, Associate Professor at Southwest Texas State University.

iix) Visiting Professor at the University of Brasilia, January-February 1979.

  1. ix) From September 1977 to August 1980, Associate Professor at the Centro de Investigación del I.P.N. (Mexico); Associate Chair 1978-80. From September 1980 to May 1983, Professor of Mathematics at the same University.

PRINCIPAL SPEAKER AT PROFESSIONAL MEETINGS.

First Latin-American School of Differential Equations, Five lectures on \The Reduction Method via Minimax”. (Brasil, July 1981). First Latin American Meeting in Applied Mathematics, Three lectures on \Minimax Methods and Nonlinear Problems” (Chile, December 1981). First Colombian Symposium in Functional Analysis, Three lectures on \Variational Methods” (Medellín-Colombia, August 1981). Course on Variational Methods of the International Center for Theoretical Physics (Trieste, November, 1981), Five lectures on \Variational Methods”. Lectures on Nonlinear problems at the College on Variational Methods and Analysis (International Centre for Theoretical Physics, Trieste, January 1988). Second Latin American Meeting in Analysis, Bogota-Colombia, November 1992, \Problemas elipticos semilineales”. Mississippi State University Annual Conference on Differential Equations, \Bifurcation and Radial Solutions to Boundary Problems”, March 19/93.\Semipositone Problems”, Keynote Address at the Annual Meeting of the Venezuelan Mathematical Society, Barquisimeto March 1994. \Five Lectures in Nonlinear Functional Analyis”, 1994 Summer School, Medellin Colombia. \Five lectures on degree theory”, 2nd. Colloqium in Differential Equations, Maracabio Venezuela, Mayo 1995. \Sign-Changing Solutions for Semilinear Dirichlet Problems”, Conference on Di_erential Equations and Harmonic Analysis honoring Professor Victor Shapiro, Riverside California, November 1995. \Ekeland Principle and Applications”, III Colloqium in Differential Equations, Maracabio Venezuela, May 1997. \Sign-changing Solutions for Second Order Elliptic Equations”, First Georgia Southern Conference on Differential Equations and Computational Mathematics, Statesboro (Georgia), April 1, 2000. \Sign changing solutions for semilinear boundary value problems”, SEARCDE, Wake Forest University, November 4, 2001. \Nonradial solutions for superlinear problems”, Latin American School of Mathematics, Cartagena (Colombia), August 2002. Invited as principal speaker for the Eighth Mississippi State – UAB Conference on Differential Equations & Computational Simulations (May, 2009), Keynote speaker at the 10th. Conference on Differential Equations & Computational Simulations (May, 2009), Keynote speaker at the Colombian Congress of Mathematics, (July, 2015).

DOCTORAL STUDENTS:

Mario Zuluaga (Centro de Investigación del I.P.N., Mexico, June 1982), Alexandra Kurepa (North Texas State University, Denton, July 1987), Sumalee Unsurangsie (North Texas State University, Denton, March 1988), Ismael Ali (University of North Texas, Denton, November 1990), Jorge Cossio (University of North Texas, Denton, November 1991), Sudhasree Gadam (University of North Texas, Denton, August 1992), Mehran Hassanpour (University of North Texas, Denton, June 1995), John M. Neuberger (University of North Texas, Denton, June 1995), Jose F. Caicedo (Universidad Nacional de Colombia, Bogotá, December 1996), Marcel Finan (North Texas State University, Denton, July1998), Hugo Aduén, (Universidad Nacional de Colombia, Medellín, March 2005), Carlos A. Velez (Universidad Nacional de Colombia, Medellín, July 2008), Rodrigo Duque (Universidad Nacional de Colombia, Bogotá, September 2011), Víctor Ardila (Universidad Nacional de Colombia, Bogotá, May 2014) , and Arturo Sanjuan (Universidad Nacional de Colombia, Bogotá, February 2015).

PROFESSIONAL SERVICE.

Member of the Editorial Board of of Revista Colombiana de Matemáticas, International Journal of Mathematics, and Communication on Nonlinear Analysis. Co-organizer of the 1983, 1986, 1992, 1997 and 2002 Texas Seminar in Differential Equations. Chair of the Human Right Committee of the American Mathematical Society (2008-09). Representative of the American Mathematical Society at the Committee on Undergraduate Programs in Mathematics (2007-10). Member of the Books Donation Committee of the AMS.

THE ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS

Co-founder and Managing Editor of the Electronic Journal of Di_erential Equations. This is a pioneering journal in paperless publication. It publishes in excess of 150 research papers per year, in addition to several monographs and proceedings of conferences. Since its inception it has been made accessible free of charge via the Internet.

Premios y reconocimientos recibidos

Ford Foundation Fellowship (National University of Colombia 1973). Laws Fellowship (University

of Cincinnati 1974-1975). Taft Fellowship (University of Cincinnati, 1976-1977). Lefschetz Instructorship

(Centro de Investigacion del I.P.N., Mexico, 1977-78). Conacyt Grant PNCB 236 (Mexico,

1980-82). Visiting Professor at Argonne National Laboratory (May-July 1987). NSF Grant No.

INT-8704327 to participate in the US-Colombia Mathematics Meeting (Bogota, July 1987).Texas

Advanced Research Program Grant (May 1988-August 1989). Texas Advanced Research Program

Grants (1989-1990 and 1990-1991). National Science Foundation Grants No DMS-8905936, DMS-

9215027, INT-9631897, CSEMS-9987215, and OISE-0703715. Sloan/CGE grant to study the feasibility

of a Professional Masters Degree. Simons Foundation grant (September 2012 to August

2017).

 

Publicaciones (lista completa)

RESEARCH PUBLICATIONS

  1. \Condiciones su_cientes para la existencia de soluciones debiles del problema de fontera Lu =

g(u(x); x) x 2 D, u(x) = 0 x 2 @D,” Revista Colombiana de Matematicas, Vol. IX (1975), pp.

173-187.

  1. (With A.C. Lazer), \Critical point theory and the number of solutions of a nonlinear Dirichlet

problem,” Annali di Mat. Pura et App. , Vol CXX (1979), pp. 113-137.

  1. (With A.C. Lazer), \Applications of a max-min principle,” Revista Colombiana de Matematicas,

Vol. X (1976), pp. 141-149.

  1. \Hammerstein integral equations with inde_nite kernel,” Internat. J. Math. and Math. Sci., Vol

1 (1978), pp. 187-201.

  1. \A semilinear Dirichlet problem” Canadian J. of Math., Vol. XXXI, No. 2(1979), pp. 337-340.
  2. \A two point boundary value problem with jumping nonlinearities,” Proc. Am. Math. Soc., Vol.

79, No. 2 (1980), pp. 207-211.

  1. (With P.W. Bates), \Existence and uniqueness for a variational hyperbolic system without reso-

nance” Nonlinear Analysis TMA, Vol. 4, No. 6(1980), pp. 1151-1156.

  1. (With P.W. Bates), \Necessary and su_cient conditions for existence of solutions to equations

with noninvertible linear part,” Rev, Colombiana de Mat., Vol XV (1981), pp. 7-24.

  1. \Periodic solutions of the forced pendulum equation,” Di_erential Equations (Editors S. Ahmad,

A.C. Lazer and M. Keener), Academic Press (1980), pp. 149-160.

  1. (With A.C. Lazer), \On periodic solutions of weakly coupled systems of di_erential equations,”

Boll. Un. Mat. Ital., (5), 18-B(1981), pp. LS733-742.

  1. \Existence of in_nitely many solutions for a class of superlinear problems,” Bol. Soc. Mat.

Mexicana, Vol. 26, No. 1 (1981), pp. 7-12.

  1. \Reduction method via minimax,” survey paper in Di_erential equations, Lecture Notes in

Mathematics, Springer Verlag (1982), pp. 1-20.

  1. (With J.V. Goncalves), \On multiple solutions of nonlinear elliptic equations with odd nonlin-

earities,” Di_erential Equations, Lecture Notes in Mathematics No. 957. Springer Verlag (1982),

  1. 21-33.
  2. (With A.C. Lazer), \Results on periodic solutions of parabolic equations suggested by elliptic

theory,” Boll. Un. Mat. Ital., (6), 1-B (1982), pp. 1089-1104.

2

  1. (With R. Shivaji), \Uniqueness of positive solutions for a class of elliptic boundary value prob-

lems,” Proc. of the Royal Soc. of Edinburgh, 98A (1984), pp. 267-269.

  1. \On the steepest descent for nonpotential locally Lipschitzian vector _elds,” Houston J. of Math

., Vol 11(1985), pp. 45-48.

  1. \Uniqueness of positive solutions for a sublinear Dirichlet problem,” Proc. Symp. on Pure Math

, Vol 45-1(1986), pp. 243-252.

  1. (With R. Shivaji), \Multiple solutions for a Dirichlet problem with jumping nonlinearities,”

Trends in the Theory and Practice of Nonlinear Analysis, North Holland (1985), pp. 97-101.

  1. (With P. Khalili), \Addendum to: Existence and uniqueness of solutions to nonlinear disspative

wave equations,” Nonlinear Analysis Theory Methods and Applications , Vol. 10, No. 12,.(1986),

  1. 1485-86.
  2. \On a Rayleigh quotient,” American Math. Monthly , Vol. 90, (1983), pp. 712-713.
  3. (With R. Shivaji) \Multiple solutions for a Dirichlet problem with jumping nonlinearities II,”

Journal of Math. Analysis and Appl . Vol. 133, No. 2 (1988) 509-528.

  1. (With A. Kurepa), \In_nitely many radially symmetric solutions to a superlinear Dirichlet

problem in a ball,” Proc. Amer. Math. Soc., Vol. 101, No. 1 (1987), pp. 57-64.

  1. (With A. Kurepa), \Energy analysis of a nonlinear singular di_erential equation,” Revista

Colombiana de Matematicas, Vol. XXI (1987), pp. 155-166.

  1. (With S. Unsurangsie), \A semilinear wave equation with nonmonotone nonlinearity,” Paci_c

Journal of Mathematics, Vol. 132, No. 2 (1988).

  1. (With R. Shivaji), \Non-negative solutions for a class of non-positone problems,” Proc. Royal

Soc. Edinburgh, 108A, (1988), pp. 291-302.

  1. (With A. Kurepa), \Radially symmetric solutions to a superlinear Dirichlet problem in a ball

with jumping nonlinearities,” Trans. Amer. Math. Soc ., Vol. 315, No. 1, (1989), pp. 353-372.

  1. (With R. Shivaji) \Non-negative solutions for a class of radially symmetric Non-positone prob-

lems”, Proc. Amer. Math. Soc. , Vol. 106, No. 3 (1989), pp. 735-740.

  1. (With K. J. Brown and R. Shivaji) \Non-existence of radially symmetric nonnegative solutions

for a class of semipositone problems”, Di_erential and Integral Equations, Vol. 2, No. 4 (1989), pp.

541-545.

  1. (With R. Shivaji), \Non-negative solutions to a semilinear Dirichlet problem in a ball are positive

and radially symmetric,” Comm. in Partial Di_erential Equations, Vol. 14, No. 8-9, (1989), pp.

1091-1100.

  1. (With I. Ali and R. Shivaji), \Uniqueness and stability of nonnegative solutions for a semiposi-

tone Dirichlet problems in the ball”, Proc. Amer. Math. Soc., Vol. 117 (1993), pp. 775-782.

  1. (With J. Garner and R. Shivaji), \Existence results for classes of sublinear semipositone prob-

lems”, Results in Mathematics, Vol. 23 (1993), pp. 214-220.

  1. (With J. Cossio), \A bifurcation theorem and applications”, Dynamic Systems and Applications,

Vol. 2 (1993), pp. 221-226.

  1. (With J. Cossio), \Multiple radial solutions for a semilinear Dirichlet problem in a ball”, Rev.

Colombiana de Matem_aticas, Vol. XXVII (1993), pp. 15-24.

  1. (With S. Gadam) \The Lazer Mckenna conjecture for radial solutions in the Rn ball”, Electronic

Journal of Di_erential Equations, Volume 1993, No. 7.

  1. (With S. Gadam), \Uniqueness of the stable and unstable positive solution for semipositone

problems”, Nonlinear Analysis T.M.A., Vol. 22, No. 4 (1994), pp. 425-429.

  1. (With A. Kurepa), \Radially symmetric solutions to a Dirichlet problem involving critical expo-

nents”, Trans. Amer. Math. Soc., Vol. 343, No. 2 (1994), pp. 907-926.

3

  1. (With J. Cossio) \Multiple solutions for a semilinear Dirichlet problem”, SIAM J. Math. Anal.,

Vol. 25 (1994), pp. 1554-1561.

  1. (With S. Gadam and R. Shivaji) \Branches of radial solutions for semipositone problems”, J.

Di_erential Equations, Vol. 120, No. 1 (1995), pp. 30-45.

  1. (With M. Hassanpour and R. Shivaji) \Uniqueness of nonnegative solutions for a semipositone

problem with concave nonlinearity”, Comm. Partial Di_erential Equations, Vol 20, No. 11-12 (1995),

  1. 1927-1936.
  2. (With I. Ali) \Positive solutions for a semilinear elliptic problem with critical exponent”, Nonlinear

Analysis T.M.A., Vol. 27, No. 3 (1996), pp. 327-338.

  1. (With A. Kurepa) \Radial solutions to a Dirichlet problem involving critical exponents when

N=6″, Trans. Amer. Math. Soc., Vol. 348, No. 2 (1996), pp. 781-798.

  1. (With V. Anuradha and R. Shivaji) \Existence results for semipositone systems”, Journal of

Dynamic Systems and Applications, Vol. 5, No. 2, (1996), pp. 219-228.

  1. (With J. Cossio and J. M. Neuberger) \A sign-changing solution for a superlinear Dirichlet

problem”, Rocky Mountain Journal of Mathematics, Vol. 27, No. 4 (1997), pp. 1041-1053.

  1. (With Jose F. Caicedo) \A semilinear wave equation with derivative of nonlinearity containing

multiple eigenvalues of in_nite multiplicity”, Contemporary Mathematics, Vol. 208 (1997), pp. 111-

132.

  1. (With S. Gadam and R. Shivaji) \Positive solutions curves of semipositone problems with

concave nonlinearities”, Proc. Royal Society of Edinburgh, Vol. 127A (1997), pp. 921-934.

  1. (With Jorge Cossio and John M. Neuberger) \On multiple solutions of a nonlinear Dirichlet

problem”, Nonlinear Analysis TMA, Vol.30, No. 6 (1997), pp. 3657-3662.

47 (Wtih J. Cossio) \El principio variacional de Ekeland, rango de operadores no lineales y una

ecuaci_on de onda semilineal”, III Coloquio sobre ecuaciones di_erenciales y sus aplicaciones, Universidad

del Zulia, Venezuela (1997).

  1. (With J. Cossio and J. M. Neuberger) \A Minmax principle, index of the critical point, and

existence of sign changing solutions to elliptic boundary value problems”, Electronic Journal of Differential

Equations (http://ejde.math.swt.edu), Vol. 1998 (1998), No. 2, pp. 1-18.

  1. (With R. Shivaji) \Positive solutions for a concave semipositone Dirichlet problem”, Nonlinear

Analysis TMA, Vol. 31, No. 1-2 (1998), pp. 91-98.

  1. (With H. Kuiper) \On the number of radially symmetric solutions to Dirichlet problems with

jumping nonlinearities of superlinear order”, Transactions of the Amer. Math. Soc., Vol. 351, No.

5 (1999), 1919-1945.

  1. (With M. Finan) \Existence of many sign-changing solutions to a superlinear Dirichlet problem

on thin annuli”, Topological Methods in Nonlinear Analysis. Vol.13, No.2, (1999), pp. 273-280.

  1. (With John W. Neuberger) \An inverse function theorem”, Contemporary Mathematics, Vol.

221 (1999), 127-132.

  1. (With S. Gadam and R. Shivaji) \Evolution of positive solutions curves of semipositone problems

with concave nonlinearities”, Journal of Mathematical Analysis and Applications, 245 (2000), pp.

282-293.

  1. (With C. Maya and R. Shivaji) \An existence result for a class of sublinear semipositone

systems”, Dynamics of Continuous, Discrete and Impulsive Systems, Volume 7, Number 4 (2000),

  1. 533-540.
  2. (With M. Finan) \Existence of many positive solutions to a superlinear Dirichlet problem on

thin annuli”, Nonlinear Di_erential Equations, Electron. J. Di_. Eqns., Conf. 05 (2000), pp. 21-31.

4

  1. (With J. W. Neuberger) \A inverse function theorem via continuous Newton’s method”, Nonlinear

Analysis 47 (2001), pp. 3223-3229.

  1. (With C. Maya and R. Shivaji) \Positivity of nonnegative solutions for cooperative semipositone

systems”, Proceedings of Dynamic Systems and Applications, Volume 3, (2001), 113-120.

  1. (With J. W. Neuberger) \A local inversion principle of the Nash-Moser type”, SIAM J. Math.

Analysis, Vol. 33, No. 4 (2001), pp. 989-993.

  1. (With H. Adu_en) \In_nitely many nonradial solutions to a superlinear Dirichlet Problem”, Proc.

Amer. Math. Soc. 131 (2003), 835-843.

  1. \In_nitely many solutions for a superlinear Neumann Problem in tilable regions”, Evolution

Equations, Lecture Notes in Pure and Applied Mathematics, Marcel Decker Inc., Vol. 234, 2003,

pp.71-76.

  1. (With M. Clapp) \The e_ect of the domain topology on the number of sign changing solutions

of an elliptic equation with critical nonlinearity”, Nonlinearity 16(2003), 579-590.

  1. (With Pavel Drabek and John M. Neuberger) \A sign-changing solution for a superlinear

Dirichlet problem”, Electron. J. Di_. Eqns., http://ejde.math.swt.edu, Conf. 10, 2003, pp. 101-107.

  1. (With C. Chang) \Asymptotic behavior of the potential and existence of a periodic solution for

a second order di_erential equation”, Applicable Analysis, Vol. 82, No. 11, November 2003, pp.

1029-1038.

  1. (With M Chhetri and R. Shivaji) \Stability Analysis of Positive Solutions to Classes of Reaction-

Di_usion Systems”, Di_erential and Integral Equations, 17 (2004), No. 3-4, pp. 391-406.

  1. \Semilinear equations with discrete spectrum”, Contemporary Mathematics, 357 (2005), pp.

1-16.

  1. (With J. Cossio) \Construction of a Radial Solution to a Superlinear Dirichlet Problem that

Changes Sign Exactly Once “, Progress in Nonlinear Di_erential Equations, Vol. 66 (2005), 149-160.

  1. (With M. Clapp) \Upper estimates for the energy of solutions of nonhomogeneous boundary

value problems”, Proc. Amer. Math. Soc. 134 (2006), no. 1, 167{175.

  1. (With S. Caldwell, R. Shivaji, and S. Unsurangsie) \Positive solutions for classes of multiparam-

eter elliptic semipositone problems”, Electronic Journal of Di_erential Equations, Vol. 2007(2007),

No. 96 pp. 1-10.

  1. (With J. Kwon and C. M. Tan) \In_nitely many radial solutions for a sub-super critical Dirichlet

boundary value problem in a ball”, Electronic Journal of Di_erential Equations, Vol. 2007(2007),

No. 111 pp. 1-10.

  1. (With H. Adu_en and J. Cossio) \Uniqueness of large radial solutions and existence of nonradial

solutions for a superlinear Dirichlet problem in annulii”, Journal of Mathematical Analysis and

Applications, Vol. 337 (2008), pp. 348-359.

  1. (With J. F. Caicedo) \A semilinear wave equation with smooth data and no resonance having no

continuous solution,” Discrete and Continuous Dynamical Systems, Vol. 24, (2009), pp. 653-658.

  1. (With V. Padr_on) \Classi_cation of radial solutions arising in the study of thermal structures

with thermal equilibrium or no ux at the boundary,” Memoirs of the Amer. Math. Soc. 208,

(2010), pp. 1-88.

  1. (With B. Preskill)\Existence of solutions for a semilinear wave equation with non-monotone

nonlinearity, Continuous and Discrete Dynamical Systems, Series A, Vol. 28, No. 2, (2010), pp.

649-658.

  1. \Nonexistence of Continuous Solutions for a Semilinear Wave Equations with Smooth Data,

Water Waves, ed. M. F. Mahmood, D. Henderson and H. Segur, World Scienti_c (2010).

5

  1. (With C. Chang) \A Variational Characterization of the Fucik Spectrum and Applications”,

Revista Colombiana de Matem_aticas, Vol. 44, No. 1, (2010), pp. 23-40.

  1. (With J.F. Caicedo and R. Duque) \Existence of Solutions for a Wave Equation with Non-

monotone Nonlinearity and a Small Parameter”, Milan Journal of Mathematics, Volume 79, Number

1, (2011), pp. 207-220.

  1. (With J. Cossio and C. Velez ) \Existence and Qualitative Properties of Solutions fo Nonlinear

Dirichlet Problems”, Discrete and Continuous Dynamical Systems, Volume 33, Number 1, January

2013, doi:10.3934/dcds.2013.33.123

  1. (With J. Cossio and C. Velez) \Existence of seven solutions for an asymptotically linear Dirichlet

problem without symmetries”, Ann. Mat. Pura Appl. (4) 192 (2013), no. 4, 607-619.

  1. (With L. Sankar and R. Shivaji) \Uniqueness of Nonnegative Solutions for Semipositone Prob-

lems on Exterior Domains”, J. Math. Anal. Appl. 394 (2012), no. 1, 432-437.

  1. (With R. Pardo) \Resonant solutions and turning points in an elliptic problem with oscillatory

boundary conditions, Paci_c J. Math. 257 (2012), no. 1, 75-90.

  1. (With E. Ko and R. Shivaji) \A uniqueness result for a singular nonlinear eigenvalue problem”,

Proc. Roy. Soc. Edinburgh Sect. A 143 (2013), no. 4, 739-744.

  1. (,With J. Caicedo, R. Duque and A. Sanjun) \Arturo Existence of Lp-solutions for a semilinear

wave equation with non-monotone nonlinearity”, Discrete Contin. Dyn. Syst. Ser. S 7 (2014), no.

6, 1193-1202.

  1. (With V. Ardila and J. Caicedo), \Existence of non-degenerate continua of singular radial

solutions for several classes of semilinear elliptic problems”, Milan J. Math. 82 (2014), no. 2,

313-330.

  1. (With J.C. Carde~no), \Existence of positive solutions for a superlinear elliptic system with

Neumann boundary condition”, Proceedings of the Variational and Topological Methods: Theory,

Applications, Numerical Simulations, and Open Problems, 23-30, Electron. J. Di_er. Equ. Conf.,

21.

  1. (With R. Pardo), \A priori bounds for positive solutions of subcritical elliptic equations”, Rev.

Mat. Complut. 28 (2015), no. 3, 715-731.

  1. (With E. Fischer), \In_nitely many rotationally symmetric solutions to a class of semilinear

Laplace-Beltrami equations on spheres”, Canad. Math. Bull. 58 (2015), no. 4, 723-729.

  1. (With R. Pardo) \Branches of positive solutions of subcritical elliptic equations in convex do-

mains”, Discrete Contin. Dyn. Syst. (2015), Dynamical systems, di_erential equations and applications.

10th AIMS Conference. Suppl., 230-238.

  1. (With V. Padr_on) \Existence of in_nitely many continua of radial singular polytropes with gain-

loss function”, Contributions to nonlinear elliptic equations and systems, 77-86, Progr. Nonlinear

Di_erential Equations Appl., 86, Birkhuser/Springer, (2015).

  1. (With. R. Pardo) \Branches of positive solutions for subcritical elliptic equations”, Contributions

to nonlinear elliptic equations and systems, 87-97, Progr. Nonlinear Di_erential Equations Appl.,

86, Birkhuser/Springer, (2015).

  1. (With D.G. de Figueiredo and E. Lopera) \Existence of positive solutions for a semipositone

p-Laplacian problem”, Proc. Roy. Soc. Edinburgh Sect. A 146 (2016), no. 3, 475-482.

  1. (With I. Ventura) \Existence of solutions to a semilinear elliptic boundary value problem with

augmented Morse index bigger than two”, Topol. Methods Nonlinear Anal. 49 (2017), no. 1,

233-244.

  1. (With G. Reyes) \Existence of multiple solutions for a semilinear problem and a counterexample

by E. N. Dancer.”, Commun. Pure Appl. Anal. 16 (2017), no. 4, 1135-1145.

6

  1. (With R. Pardo) \A priori estimates for positive solutions to subcritical elliptic problems in a

class of non convex regions”, Discrete Contin. Dyn. Syst. Ser. B 22 (2017), no. 3, 783-790.

  1. (With J. Caicedo and A. Sanjuan) \Bifurcation at in_nity for a semilinear wave equation with

non-monotone nonlinearity”, Discrete Contin. Dyn. Syst. 37 (2017), no. 4, 1857-1865.

  1. (With. R. Pardo) \In_nitely many stability switches in a problem with sublinear oscillatory

boundary conditions”, J. Dynam. Di_erential Equations 29 (2017), no. 2, 485-499.

  1. (With. R. Shivaji and D. Costa) \Multiple positive solutions for a class of variational systems”,

Topol. Methods Nonlinear Anal. 50 (2017), no. 1, 1?8.

OTHER PUBLICATIONS

  1. \M_etodos variacionales en An_alisis Funcional No Lineal,” monograph published by the Colombian

Math. Soc., (1980).

  1. \M_etodos de reducci_on via minimax,” monograph published by the University of Sao Paulo

(Brasil) (1981).

  1. (With Saul Hahn) \Ecuaciones Diferenciales Parciales,” monograph published by the Centro de

Investigacion del I.P.N. (Mexico).

  1. \Introduccion al Estudio de Ecuaciones Di_erenciales no Lineales con Condicion de Frontera”,

Universidad Nacional de Colombia (1992).

  1. (With R. Shivaji) \Semipositone Problems,” Semigroups of Nonlinear Operations and Applications,

(1993), pp. 109-119.

  1. \Bifurcation Theory and Radial Solutions to Elliptic Bounday Value Problems,” Applied Mathematics

and Computation 65 (1994), pp. 223-230.

  1. (With Jorge Cossio) \Soluciones no triviales para un problema de Dirichlet superlineal sin

Simetr__as,” Memorias de la Escuela de Verano, Medell__n Colombia (1994).

  1. \Review of Solvability and Bifurcation of Nonlinear Equations by P. Drabek.” Siam Review, Vol.

36, No. 1, (1994), 119-121.

  1. (With I. Ali Taqi) \Regularity for an elliptic problem”, Rev. Tec. Univ. Zulia, Vol. 17, No. 1

(1994), pp. 43-45.

  1. (With J. Cossio) \El principio variacional de Ekeland, rango de operadores no lineales y una

ecuaci_on de onda semilieal”, Memorias del II Coloquio en Ecuaciones Diferenciales, Maracaibo

(1977).

  1. \Ecuaciones diferenciales el__pticas semilineales”, Memorias III Escuela de Verano Geometr__a

Diferencial, Ecuaciones Diferenciales Parciales y An_alisis Nem_erico, Academia Colombiana de Ciencias

(1996).

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