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

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 $|s| o+infty$. We establish the existence of two distinct solutions when the perturbation is suitable small.