On a class of semilinear elliptic problems near critical growth - J. V. Goncalves; S. Meira (International Journal of Mathematics and Mathematical Sciences)
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.