Minimax principles for critical-point theory in applications to quasilinear boundary-value problems

Abstract

Using the variational method developed by the same author in [7], we establish the existence of solutions to the equation $-Delta_p u = f(x,u)$ with Dirichlet boundary conditions. Here $Delta_p$ denotes the p-Laplacian and $int_0^s f(x,t),dt$ is assumed to lie between the first two eigenvalues of the p-Laplacian.

Keywords

• Minimax methods
• p-Laplacian
• resonance.