International Journal of Mathematics and Mathematical Sciences 
Volume 21 (1998), Issue 2, Pages 321-330
doi:10.1155/S0161171298000441

On a class of semilinear elliptic problems near critical growth

J. V. Goncalves1 and S. Meira2

 1Departamento de Matemática, Universidade de Brasilia, Brasilia 70910-900, DF, Brazil
2Departamento de Matemática, Unesp- Presidente Prudente, Presidente Prudente, SP, Brazil
Received 17 May 1996; Revised 30 January 1997

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.