International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 2, Pages 321-330

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

Copyright © 1998 J. V. Goncalves and S. Meira. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.