Kanishka Perera
Professor
Department of Mathematical Sciences
Florida Institute of Technology
150 West University Boulevard
Melbourne, FL 32901-6975
kperera@fit.edu
Variational and topological methods for nonlinear partial differential equations:
semilinear and quasilinear elliptic boundary value problems, problems with singularities, critical point theory, infinite dimensional Morse theory
Professor, Florida Institute of Technology, 2007-Present
Associate Professor, Florida Institute of Technology, 2002-2006
Assistant Professor, Florida Institute of Technology, Spring 2000-2001
Visiting Assistant Professor, University of California, Irvine, 1997-1999
Visiting Assistant Professor, Stevens Institute of Technology, New Jersey, Spring 1997
Instructor, Courant Institute, New York University, 1994-Fall 1996
Visiting Professor, Stockholm University, Sweden, Summer 2003
Visiting Scholar, University of Sydney, Australia, Summer 2000
Visiting Scholar, Chinese Academy of Sciences, Beijing, Fall 1999
Associate Editor, Advances in Difference Equations
Associate Editor, Boundary Value Problems
Reviewer, Mathematical Reviews (MR)
Ph.D., Mathematics, Courant Institute, New York University, 1996
B.S., Mathematics, Stevens Institute of Technology, New Jersey, 1992
| [1] |
Positive solutions of multiparameter semipositone p-Laplacian problems (with Ratnasingham Shivaji)
J. Math. Anal. Appl. 338 (2008), no. 2, 1397-1400 |
| [2] |
Positive solutions in the sense of distributions of singular boundary value problems (with Ravi P. Agarwal and Donal O'Regan)
Proc. Amer. Math. Soc. 136 (2008), no. 1, 279-286 |
| [3] |
Existence and nonexistence results for a class of quasilinear elliptic systems (with Said El Manouni)
Boundary Value Problems 2007 (2007), Article ID 85621, 5 pages |
| [4] |
Nonlinear integral equations singular in the dependent variable (with Ravi P. Agarwal and Donal O'Regan)
Appl. Math. Lett. 20 (2007), no. 11, 1137-1141 |
| [5] |
Multiple Positive Solutions of Singular Dirichlet Problems on Time Scales via Variational Methods (with Ravi P. Agarwal, Victoria Otero-Espinar, and Dolores R. Vivero)
Nonlinear Anal. 67 (2007), no. 2, 368-381 |
| [6] |
Existence of Multiple Positive Solutions for
Second Order Nonlinear Dynamic BVPs by Variational Methods (with Ravi P. Agarwal, Victoria Otero-Espinar, and Dolores R. Vivero)
J. Math. Anal. Appl. 331 (2007), no. 2, 1263-1274 |
| [7] |
Sandwich pairs in p-Laplacian problems (with Martin Schechter)
Topol. Methods Nonlinear Anal. 29 (2007), no. 1, 29-34 |
| [8] |
On singular p-Laplacian problems (with Elves A. B. Silva)
Differential Integral Equations 20 (2007), no. 1, 105-120 |
| [9] |
p-Laplacian problems with critical Sobolev exponents (with Elves A. B. Silva)
Nonlinear Anal. 66 (2007), no. 2, 454-459 |
| [10] |
A variational approach to singular quasilinear elliptic problems with sign changing nonlinearities (with Ravi P. Agarwal and Donal O'Regan)
Appl. Anal. 85 (2006), no. 10, 1201-1206 |
| [11] |
Existence and multiplicity of positive solutions for singular quasilinear problems (with Elves A. B. Silva)
J. Math. Anal. Appl. 323 (2006), no. 2, 1238-1252 |
| [12] |
Basic properties of Sobolev's spaces on time scales (with Ravi P. Agarwal, Victoria Otero-Espinar, and Dolores R. Vivero)
Adv. Difference Equ. 2006 (2006), Art. ID 38121, 14 pp. |
| [13] |
Sign changing solutions of Kirchhoff type problems via invariant sets of descent flow (with Zhitao Zhang)
J. Math. Anal. Appl. 317 (2006), no. 2, 456-463 |
| [14] |
Nontrivial solutions of Kirchhoff type problems via the Yang index (with Zhitao Zhang)
J. Differential Equations 221 (2006), no. 1, 246-255 |
| [15] |
Multiple positive solutions of singular problems by variational methods (with Ravi P. Agarwal and Donal O'Regan)
Proc. Amer. Math. Soc. 134 (2006), no. 3, 817-824 |
| [16] |
Multiple positive solutions of singular p-Laplacian problems via variational methods (with Elves A. B. Silva)
Proceedings of the Conference on Differential and Difference Equations and Applications, 915-924, Hindawi Publ. Corp., 2005 |
| [17] |
Multiple positive solutions of singular p-Laplacian problems by variational methods (with Zhitao Zhang)
Boundary Value Problems 2005
(2005), no. 3, 377-382 |
| [18] |
Positive solutions of higher order singular problems (with Ravi P. Agarwal and Donal O'Regan)
Differential Equations 41 (2005), no. 5, 739-743 |
| [19] |
Multiple positive solutions of singular discrete p-Laplacian problems via variational methods (with Ravi P. Agarwal and Donal O'Regan)
Adv. Difference Equ. 2005 (2005), no. 2, 93-99 |
| [20] |
p-Laplacian problems where the nonlinearity crosses an eigenvalue (with Andrzej Szulkin)
Discrete Contin. Dyn. Syst. 13 (2005), no. 3, 743-753 |
| [21] |
On the Fucik spectrum of the p-Laplacian
NoDEA Nonlinear Differential Equations Appl. 11 (2004), no. 2, 259-270 |
| [22] |
Multiple positive solutions of singular and nonsingular discrete problems via variational methods (with Ravi P. Agarwal and Donal O'Regan)
Nonlinear Anal. 58 (2004), no. 1-2, 69-73 |
| [23] |
p-Superlinear problems with jumping nonlinearities
Nonlinear analysis and applications: to V. Lakshmikantham on his 80th birthday. Vol. 1, 2, pages 823--829. Kluwer Acad. Publ., Dordrecht, 2003 |
| [24] |
Nontrivial solutions of p-superlinear p-Laplacian problems
Appl. Anal. 82 (2003), no. 9, 883-888 |
| [25] |
Nontrivial critical groups in p-Laplacian problems via the Yang index
Topol. Methods Nonlinear Anal. 21 (2003), no. 2, 301-309 |
| [26] |
Computation of critical groups in Fucik resonance problems (with Martin Schechter)
J. Math. Anal. Appl. 279 (2003), no. 1, 317-325 |
| [27] |
Double resonance problems with respect to the Fucik spectrum (with Martin Schechter)
Indiana Univ. Math. J. 52 (2003), no. 1, 1-17 |
| [28] |
Multiple positive solutions for a class of quasilinear elliptic boundary value problems
Electron. J. Differential Equations 2003 (2003), no. 7, 1-5 |
| [29] |
Sign-changing and multiple solutions for the p-Laplacian (with Siegfried Carl)
Abstr. Appl. Anal. 7 (2002), no. 12, 613-625 |
| [30] |
An existence result for a class of quasilinear elliptic boundary value problems with jumping nonlinearities
Topol. Methods Nonlinear Anal. 20 (2002), no. 1, 135-144 |
| [31] |
Critical groups in saddle point theorems without a finite dimensional closed loop (with Martin Schechter)
Math. Nachr. 243 (2002), 156-164 |
| [32] |
Resonance problems with respect to the Fucik spectrum of the p-Laplacian
Electron. J. Differential Equations 2002 (2002), no. 36, 1-10 |
| [33] |
One-sided resonance for quasilinear problems with asymmetric nonlinearities
Abstr. Appl. Anal. 7 (2002), no. 1, 53-60 |
| [34] |
On the role played by the Fucik spectrum in the determination of critical groups in elliptic problems where the asymptotic limits may not exist (with Shujie Li and Jiabao Su)
Nonlinear Anal. 49 (2002), no. 5, 603-611 |
| [35] |
Computation of critical groups in resonance problems where the nonlinearity may not be sublinear (with Shujie Li)
Nonlinear Anal. 46 (2001), no. 6, 777-787 |
| [36] |
Solution of nonlinear equations having asymptotic limits at zero and infinity (with Martin Schechter)
Calc. Var. Partial Differential Equations 12 (2001), no. 4, 359-369 |
| [37] |
Computation of critical groups in elliptic boundary value problems where the asymptotic limits may not exist (with Shujie Li and Jiabao Su)
Proc. Roy. Soc. Edinburgh Sect. A 131 (2001), no. 3, 721-732 |
[38] |
Applications of Morse theory to the solution of semilinear problems depending on C1 functionals (with Martin Schechter)
Nonlinear Anal. 45 (2001), no. 1, 1-9 |
| [39] |
The Fucik spectrum and critical groups (with Martin Schechter)
Proc. Amer. Math. Soc. 129 (2001), no. 8, 2301-2308 |
| [40] |
Some remarks on the Fucik spectrum of the p-Laplacian and critical groups (with Norman Dancer)
J. Math. Anal. Appl. 254 (2001), no. 1, 164-177 |
| [41] |
A generalization of the Amann-Zehnder theorem to nonresonance problems with jumping nonlinearities (with Martin Schechter)
NoDEA Nonlinear Differential Equations Appl. 7 (2000), no. 4, 361-367 |
| [42] |
Multiple nontrivial solutions of elliptic semilinear equations (with Martin Schechter)
Topol. Methods Nonlinear Anal. 16 (2000), no. 1, 1-15 |
| [43] |
Nontrivial solutions of elliptic semilinear equations at resonance (with Martin Schechter)
Manuscripta Math. 101 (2000), no. 3, 301-311 |
| [44] |
A critical point theorem with a relaxed boundary condition and critical groups
Nonlinear Anal. 39 (2000), no. 6, 685-692 |
| [45] |
Existence and multiplicity results for a Sturm-Liouville equation asymptotically linear at negative infinity and superlinear at positive infinity
Nonlinear Anal. 39 (2000), no. 6, 669-684 |
| [46] |
Semilinear elliptic equations having asymptotic limits at zero and infinity (with Martin Schechter)
Abstr. Appl. Anal. 4 (1999), no. 4, 231-242 |
| [47] |
Applications of local linking to asymptotically linear elliptic problems at resonance
NoDEA Nonlinear Differential Equations Appl. 6 (1999), no. 1, 55-62 |
| [48] |
Critical groups of critical points produced by local linking with applications
Abstr. Appl. Anal. 3 (1998), nos. 3-4, 437-446 |
| [49] |
Type (II) regions between curves of the Fucik spectrum and critical groups (with Martin Schechter)
Topol. Methods Nonlinear Anal. 12 (1998), no. 2, 227-243 |
| [50] |
Homological local linking
Abstr. Appl. Anal. 3 (1998), nos. 1-2, 181-189 |
| [51] |
Morse index estimates in saddle point theorems without a finite-dimensional closed loop (with Martin Schechter)
Indiana Univ. Math. J. 47 (1998), no. 3, 1083-1095 |
| [52] |
Critical groups of pairs of critical points produced by linking subsets
J. Differential Equations 140 (1997), no. 1, 142-160 |
| [53] |
Multiplicity results for some elliptic problems with concave nonlinearities
J. Differential Equations 140 (1997), no. 1, 133-141 |
| [54] |
Flows and critical points (with Martin Schechter)
NoDEA Nonlinear Differential Equations Appl., to appear |
| [55] |
Wirtinger's inequalities on time scales (with Ravi P. Agarwal, Victoria Otero-Espinar, and Dolores R. Vivero)
Canad. Math. Bull., to appear |
| [56] |
Sandwich pairs for p-Laplacian systems (with Martin Schechter)
J. Lond. Math. Soc. (2), submitted |
| [57] |
Multiple nontrivial solutions of the Neumann problem for p-Laplacian systems (with Said El Manouni)
Appl. Anal., submitted |
| [58] |
Morse Theoretic Aspects of p-Laplacian Type Operators (with Ravi P. Agarwal and Donal O'Regan)
submitted |
| [59] |
Multiple positive solutions of singular elliptic problems (with Elves A. B. Silva), in preparation |
| [60] |
On singular quasimonotone (p,q)-Laplacian systems (with Said El Manouni and Ratnasingham Shivaji), in preparation |
| [61] |
Nontrivial solutions of some quasilinear problems via a cohomological local splitting (with Anna Maria Candela and Giuliana Palmieri), in preparation |
| [62] |
Nontrivial solutions of p-superlinear p-Laplacian problems via a cohomological local splitting (with Marco Degiovanni and Sergio Lancelotti), in preparation |
Conferences
Seventh MSU-UAB Conference on Differential Equations & Computational Simulations, Birmingham, Alabama, November 1-3, 2007
Fifth International Conference on Dynamic Systems and Applications, Atlanta, Georgia, May 30-June 2, 2007
The International Conference of Hybrid Systems and Applications, Lafayette, Louisiana, May 22-26, 2006
Twelfth International Conference of the Forum for Interdisciplinary Mathematics on Statistics, Combinatorics, Mathematics & Applications, Auburn, Alabama, December 2-4, 2005
Conference on Differential & Difference Equations and Applications, Melbourne, Florida, August 1-5, 2005
Topological and Variational Methods for Differential Equations, Mathematisches Forschungsinstitut Oberwolfach, Germany, June 26-July 2, 2005
Sixth MSU-UAB Conference on Differential Equations & Computational Simulations, Starkville, Mississippi, May 13-14, 2005
Twenty Fourth Annual Southeastern-Atlantic Regional Conference on Differential Equations, Chattanooga, Tennessee, October 22-23, 2004
Fourth World Congress of Nonlinear Analysts, Orlando, Florida, June 30-July 7, 2004
Twenty First Annual Southeastern-Atlantic Regional Conference on Differential Equations, Winston-Salem, North Carolina, November 2-3, 2001
Colloquium talks
Mississippi State University, 11/05/07
Georgia Southern University, 11/30/05
Mississippi State University, 10/13/05
University of Sydney, Australia, 05/26/00
Capital Normal University, Beijing, 11/04/99
Beijing University, China, 10/18/99
Chinese Academy of Sciences, Beijing, 08/30/99
Utah State University, 03/25/99
University of Oklahoma, 03/08/99
Florida Institute of Technology, 03/02/99
Kansas State University, 02/25/99
University of California, Irvine, 11/04/97
Stevens Institute of Technology, New Jersey, 02/26/97
Rutgers University, New Jersey, 01/28/97
Courant Institute, New York University, 09/20/95
