On a class of semilinear elliptic problems near critical growth

Abstract

ABSTRACT. We use Minimax Methods and explore compact embedddings in the context of Orlicz and Orlicz-Sobolev spaces to get existence of weak solutions on a class of semilinear elliptic equations with nonlinearities near critical growth. We consider both biharmonic equations with Navier boundary conditions and Laplacian equations with Dirichlet boundary conditions.

Existence and multiplicity of solutions for a class of superlinear p-Laplacian equations

“…This (AR) condition usually plays a very important role in verifying that the functional corresponding to problem has a MountainPass geometry and shows that a related (PS) c sequence is bounded (see [1,2,5,12]). But there are always many functions that do not satisfy (AR) condition.…”