Electron. J. Diff. Equ., Vol. 2011 (2011), No. 98, pp. 1-13.

Existence and multiplicity of solutions for a singular semilinear elliptic problem in R^2

Manasses de Souza

Using minimax methods we study the existence and multiplicity of nontrivial solutions for a singular class of semilinear elliptic nonhomogeneous equation where the potentials can change sign and the nonlinearities may be unbounded in $x$ and behaves like $\exp(\alpha s^2)$ when $|s|\to+\infty$. We establish the existence of two distinct solutions when the perturbation is suitable small.

Submitted May 2, 2011. Published August 3, 2011.
Math Subject Classifications: 35J60, 35J20, 35B33.
Key Words: Variational methods; Trudinger-Moser inequality; critical points; critical exponents.

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Manasses de Souza
Departamento de Matemática
Universidade Federal da Paraíba
58.051-900 João Pessoa, PB, Brazil
email: manasses@mat.ufpb.br

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