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 -∆pu = ƒ(x, u) with Dirichlet boundary conditions. Here ∆p denotes the p-Laplacian and ʃs0 ƒ(x, t) dt is assumed to lie between the first two eigenvalues of the p-Laplacian.