Florida Institute of Technology
High Tech with a Human Touch
PERERA, Kanishka
Professor
Department of Mathematical Sciences, College of Science
Educational Background
Ph.D., Mathematics, Courant Institute, New York University, 1996
Professional Experience
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
Short-term Positions
Visiting Professor, Uppsala University, Sweden, Summer 2012
Visiting Professor, Università Cattolica del Sacro Cuore, Brescia, Italy, Summer 2008
Visiting Professor, Stockholm University, Sweden, Summer 2003
Visiting Professor, University of Sydney, Australia, Summer 2000
Visiting Professor, Chinese Academy of Sciences, Beijing, Fall 1999
Current Research
Noncompact variational problems, symmetry breaking, variable exponent problems
Selected Publications
[79] Perera, K., Pucci, P., Varga, C.
An existence result for a class of quasilinear elliptic eigenvalue problems in unbounded domains
arXiv:1305.2031 [math.AP].
[78] Perera, K., Squassina, M.
Asymptotic behavior of the eigenvalues of the p(x)-Laplacian
arXiv:1303.2295 [math.AP].
[77] Perera, K., Tintarev, C.
On the second minimax level for the scalar field equation
arXiv:1208.1139 [math.AP].
[76] Agarwal, R. P., Bhaskar, T. G., Perera, K.
Some results for impulsive problems via Morse theory
J. Math. Anal. Appl., to appear.
[75] Bhaskar, T. G., Perera, K.
On some elliptic interface problems with nonhomogeneous jump conditions
Adv. Nonlinear Anal. 2 (2013), no. 2, 195-211.
[74] Perera, K., Squassina, M.
On symmetry results for elliptic equations with convex nonlinearities
Commun. Pure Appl. Anal. 12 (2013), no. 6, 3013-3026.
[73] Perera, K., Schechter, M.
Morse theory applied to semilinear problems
Complex Var. Elliptic Equ. 57 (2012), no. 11, 1179-1189.
[72] El Manouni, S., Perera, K., Shivaji, R.
On singular quasi-monotone (p,q)-Laplacian systems
Proc. Roy. Soc. Edinburgh Sect. A 142 (2012), no. 3, 585-594.
[71] Agarwal, R. P., Perera, K., Zhang, Z. T.
On some nonlocal eigenvalue problems
Discrete Contin. Dyn. Syst. Ser. S 5 (2012), no. 4, 707-714.
[70] Carl, S., Perera, K.
Generalized solutions of singular p-Laplacian problems in RN
Nonlinear Stud. 18 (2011), no. 1, 113-124.
[69] Perera, K.
Morse theory and applications to variational problems
Handbook of nonconvex analysis and applications, 475-506, Int. Press, Somerville, MA, 2010.
[68] Candela, A. M., Medeiros, E. S., Palmieri, G., Perera, Kaniskha
Weak solutions of quasilinear elliptic systems via the cohomological index
Topol. Methods Nonlinear Anal. 36 (2010), no. 1, 1-18.
[67] Candela, A. M., Palmieri, G., Perera, K.
Nontrivial solutions of some quasilinear problems via a cohomological local splitting
Nonlinear Anal. 73 (2010), no. 7, 2001-2009.
[66] Perera, K., Agarwal, R. P., O'Regan, D.
Nontrivial solutions of p-superlinear anisotropic p-Laplacian systems via Morse theory
Topol. Methods Nonlinear Anal. 35 (2010), no. 2, 367-378.
[65] Degiovanni, M., Lancelotti, S., Perera, K.
Nontrivial solutions of p-superlinear p-Laplacian problems via a cohomological local splitting
Commun. Contemp. Math. 12 (2010), no. 3, 475-486.
[64] El Manouni, S., Perera, K.
Multiple non-trivial solutions of the Neumann problem for p-Laplacian systems
Complex Var. Elliptic Equ. 55 (2010), no. 5-6, 573-579.
[63] Perera, K., Agarwal, R. P., O'Regan, D.
Multiplicity results for p-sublinear p-Laplacian problems involving indefinite eigenvalue problems via Morse theory
Electron. J. Differential Equations 2010, No. 41, 6 pp.
[62] Perera, K., Silva, E. A. de B. e
Multiple positive solutions of singular elliptic problems
Differential Integral Equations 23 (2010), no. 5-6, 435-444.
[61] Medeiros, E. S., Perera, K., Tintarev, K.
Multiplicity results for problems involving the Hardy-Sobolev operator via Morse theory
Nonlinear Anal. 72 (2010), no. 5, 2170-2177.
[60] Motreanu, D., Perera, K.
Multiple nontrivial solutions of Neumann p-Laplacian systems
Topol. Methods Nonlinear Anal. 34 (2009), no. 1, 41-48.
[59] Liu, S. B., Medeiros, E. S., Perera, K.
Multiplicity results for p-biharmonic problems via Morse theory
Commun. Appl. Anal. 13 (2009), no. 3, 447-455.
[58] Medeiros, E. S., Perera, K.
Multiplicity of solutions for a quasilinear elliptic problem via the cohomological index
Nonlinear Anal. 71 (2009), no. 9, 3654-3660.
[57] Perera, K., Schechter, M.
Sandwich pairs for p-Laplacian systems
J. Math. Anal. Appl. 358 (2009), no. 2, 485-490.
[56] Perera, K., Schechter, M.
Flows and critical points
NoDEA Nonlinear Differential Equations Appl. 15 (2008), no. 4-5, 495-509.
[55] Agarwal, R. P., Otero-Espinar, V., Perera, K., Rodríguez-Vivero, D.
Multiple positive solutions in the sense of distributions of singular BVPs on time scales and an application to Emden-Fowler equations
Adv. Difference Equ. 2008, Art. ID 796851, 13 pp.
[54] Agarwal, R. P., Otero-Espinar, V., Perera, K., Rodríguez-Vivero, D.
Wirtinger's inequalities on time scales
Canad. Math. Bull. 51 (2008), no. 2, 161-171.
[53] Perera, K., Shivaji, R.
Positive solutions of multiparameter semipositone p-Laplacian problems
J. Math. Anal. Appl. 338 (2008), no. 2, 1397-1400.
[52] Agarwal, R. P., Perera, K., O'Regan, D.
Positive solutions in the sense of distributions of singular boundary value problems
Proc. Amer. Math. Soc. 136 (2008), no. 1, 279-286 (electronic).
[51] El Manouni, Said, Perera, K.
Existence and nonexistence results for a class of quasilinear elliptic systems
Bound. Value Probl. 2007, Art. ID 85621, 5 pp.
[50] O'Regan, D., Agarwal, R. P., Perera, K.
Nonlinear integral equations singular in the dependent variable
Appl. Math. Lett. 20 (2007), no. 11, 1137-1141.
[49] Agarwal, R. P., Otero-Espinar, V., Perera, K., Rodríguez-Vivero, D.
Multiple positive solutions of singular Dirichlet problems on time scales via variational methods
Nonlinear Anal. 67 (2007), no. 2, 368-381.
[48] Agarwal, R. P., Otero-Espinar, V., Perera, K., Rodríguez-Vivero, D.
Existence of multiple positive solutions for second order nonlinear dynamic BVPs by variational methods
J. Math. Anal. Appl. 331 (2007), no. 2, 1263-1274.
[47] Perera, K., Schechter, M.
Sandwich pairs in p-Laplacian problems
Topol. Methods Nonlinear Anal. 29 (2007), no. 1, 29-34.
[46] Perera, K., Silva, E. A. de B. e
On singular p-Laplacian problems
Differential Integral Equations 20 (2007), no. 1, 105-120.
[45] Perera, K., Silva, E. A. de B. e
p-Laplacian problems with critical Sobolev exponents
Nonlinear Anal. 66 (2007), no. 2, 454-459.
[44] Perera, K., Silva, E. A. de B. e
Multiple positive solutions of singular p-Laplacian problems via variational methods
Differential & difference equations and applications, 915-924, Hindawi Publ. Corp., New York, 2006.
[43] Agarwal, R. P., Perera, K., O'Regan, D.
A variational approach to singular quasilinear elliptic problems with sign changing nonlinearities
Appl. Anal. 85 (2006), no. 10, 1201-1206.
[42] Perera, K., Silva, E. A. de B. e
Existence and multiplicity of positive solutions for singular quasilinear problems
J. Math. Anal. Appl. 323 (2006), no. 2, 1238-1252.
[41] Agarwal, R. P., Otero-Espinar, V., Perera, K., Rodríguez-Vivero, D.
Basic properties of Sobolev's spaces on time scales
Adv. Difference Equ. 2006, Art. ID 38121, 14 pp.
[40] Zhang, Z. T., Perera, K.
Sign changing solutions of Kirchhoff type problems via invariant sets of descent flow
J. Math. Anal. Appl. 317 (2006), no. 2, 456-463.
[39] Perera, K., Zhang, Z. T.
Nontrivial solutions of Kirchhoff-type problems via the Yang index
J. Differential Equations 221 (2006), no. 1, 246-255.
[38] Agarwal, R. P., Perera, K., O'Regan, D.
Multiple positive solutions of singular problems by variational methods
Proc. Amer. Math. Soc. 134 (2006), no. 3, 817-824 (electronic).
[37] Perera, K., Zhang, Z. T.
Multiple positive solutions of singular p-Laplacian problems by variational methods
Bound. Value Probl. 2005, no. 3, 377-382.
[36] Agarval, R. P., Perera, K., O'Regan, D.
On positive solutions of higher-order singular problems
(Russian) Differ. Uravn. 41 (2005), no. 5, 702-705, 719; translation in Differ. Equ. 41 (2005), no. 5, 739-743.
[35] Agarwal, R. P., Perera, K., O'Regan, D.
Multiple positive solutions of singular discrete p-Laplacian problems via variational methods
Adv. Difference Equ. 2005, no. 2, 93-99.
[34] Perera, K., Szulkin, A.
p-Laplacian problems where the nonlinearity crosses an eigenvalue
Discrete Contin. Dyn. Syst. 13 (2005), no. 3, 743-753.
[33] Perera, K.
On the Fucík spectrum of the p-Laplacian
NoDEA Nonlinear Differential Equations Appl. 11 (2004), no. 2, 259-270.
[32] Agarwal, R. P., Perera, K., O'Regan, D.
Multiple positive solutions of singular and nonsingular discrete problems via variational methods
Nonlinear Anal. 58 (2004), no. 1-2, 69-73.
[31] Perera, K.
p-superlinear problems with jumping nonlinearities
Nonlinear analysis and applications: to V. Lakshmikantham on his 80th birthday. Vol. 1, 2, 823-829, Kluwer Acad. Publ., Dordrecht, 2003.
[30] Perera, K.
Nontrivial solutions of p-superlinear p-Laplacian problems
Appl. Anal. 82 (2003), no. 9, 883-888.
[29] Perera, K.
Nontrivial critical groups in p-Laplacian problems via the Yang index
Topol. Methods Nonlinear Anal. 21 (2003), no. 2, 301-309.
[28] Perera, K., Schechter, M.
Computation of critical groups in Fucík resonance problems
J. Math. Anal. Appl. 279 (2003), no. 1, 317-325.
[27] Perera, K., Schechter, M.
Double resonance problems with respect to the Fucík spectrum
Indiana Univ. Math. J. 52 (2003), no. 1, 1-17.
[26] Perera, K.
Multiple positive solutions for a class of quasilinear elliptic boundary-value problems
Electron. J. Differential Equations 2003, No. 7, 5 pp. (electronic).
[25] Carl, S., Perera, K.
Sign-changing and multiple solutions for the p-Laplacian
Abstr. Appl. Anal. 7 (2002), no. 12, 613-625.
[24] Perera, K.
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.
[23] Perera, K., Schechter, M.
Critical groups in saddle point theorems without a finite dimensional closed loop
Math. Nachr. 243 (2002), 156-164.
[22] Perera, K.
Resonance problems with respect to the Fucík spectrum of the p-Laplacian
Electron. J. Differential Equations 2002, No. 36, 10 pp. (electronic).
[21] Perera, K.
One-sided resonance for quasilinear problems with asymmetric nonlinearities
Abstr. Appl. Anal. 7 (2002), no. 1, 53-60.
[20] Li, S. J., Perera, K., Su, J. B.
On the role played by the Fucík spectrum in the determination of critical groups in elliptic problems where the asymptotic limits may not exist.
Nonlinear Anal. 49 (2002), no. 5, Ser. A: Theory Methods, 603-611.
[19] Li, S. J., Perera, K.
Computation of critical groups in resonance problems where the nonlinearity may not be sublinear
Nonlinear Anal. 46 (2001), no. 6, Ser. A: Theory Methods, 777-787.
[18] Perera, K., Schechter, M.
Solution of nonlinear equations having asymptotic limits at zero and infinity
Calc. Var. Partial Differential Equations 12 (2001), no. 4, 359-369.
[17] Li, S. J., Perera, K., Su, J. B.
Computation of critical groups in elliptic boundary-value problems where the asymptotic limits may not exist
Proc. Roy. Soc. Edinburgh Sect. A 131 (2001), no. 3, 721-732.
[16] Perera, K., Schechter, M.
Applications of Morse theory to the solution of semilinear problems depending on C1 functionals
Nonlinear Anal. 45 (2001), no. 1, Ser. A: Theory Methods, 1-9.
[15] Perera, K., Schechter, M.
The Fucík spectrum and critical groups
Proc. Amer. Math. Soc. 129 (2001), no. 8, 2301-2308 (electronic).
[14] Dancer, E. N., Perera, K.
Some remarks on the Fucík spectrum of the p-Laplacian and critical groups
J. Math. Anal. Appl. 254 (2001), no. 1, 164-177.
[13] Perera, K., Schechter, M.
A generalization of the Amann-Zehnder theorem to nonresonance problems with jumping nonlinearities
NoDEA Nonlinear Differential Equations Appl. 7 (2000), no. 4, 361-367.
[12] Perera, K., Schechter, M.
Multiple nontrivial solutions of elliptic semilinear equations
Topol. Methods Nonlinear Anal. 16 (2000), no. 1, 1-15.
[11] Perera, K., Schechter, M.
Nontrivial solutions of elliptic semilinear equations at resonance
Manuscripta Math. 101 (2000), no. 3, 301-311.
[10] Perera, K.
A critical point theorem with a relaxed boundary condition and critical groups
Nonlinear Anal. 39 (2000), no. 6, Ser. A: Theory Methods, 685-692.
[9] Perera, K.
Existence and multiplicity results for a Sturm-Liouville equation asymptotically linear at -∞ and superlinear at +∞
Nonlinear Anal. 39 (2000), no. 6, Ser. A: Theory Methods, 669-684.
[8] Perera, K., Schechter, M.
Semilinear elliptic equations having asymptotic limits at zero and infinity
Abstr. Appl. Anal. 4 (1999), no. 4, 231-242.
[7] Perera, K.
Applications of local linking to asymptotically linear elliptic problems at resonance
NoDEA Nonlinear Differential Equations Appl. 6 (1999), no. 1, 55-62.
[6] Perera, K.
Critical groups of critical points produced by local linking with applications
Abstr. Appl. Anal. 3 (1998), no. 3-4, 437-446.
[5] Perera, K., Schechter, M.
Type II regions between curves of the Fucik spectrum and critical groups
Topol. Methods Nonlinear Anal. 12 (1998), no. 2, 227-243.
[4] Perera, K.
Homological local linking
Abstr. Appl. Anal. 3 (1998), no. 1-2, 181-189.
[3] Perera, K., Schechter, M.
Morse index estimates in saddle point theorems without a finite-dimensional closed loop
Indiana Univ. Math. J. 47 (1998), no. 3, 1083-1095.
[2] Perera, K.
Critical groups of pairs of critical points produced by linking subsets
J. Differential Equations 140 (1997), no. 1, 142-160.
[1] Perera, K.
Multiplicity results for some elliptic problems with concave nonlinearities
J. Differential Equations 140 (1997), no. 1, 133-141.