Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 98, pp. 1-13.

Title: Existence and multiplicity of solutions for a singular
       semilinear elliptic problem in R^2
       
Author: Manasses de Souza (Univ. Federal da Paraiba, Brazil)

Abstract:
 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 02, 2011. Published August 03, 2011.
Math Subject Classifications: 35J60, 35J20, 35B33.
Key Words: Variational methods; Trudinger-Moser inequality; 
           critical points; critical exponents.