Localization method for the solutions of nonhomogeneous operator equations

摘要

In this paper, we prove versions of the general minimax theorem of Willem and of the Mountain Pass Theorem of Ambrosetti and Rabinowitz on a wedge intersected with a ball in a reflexive locally uniformly convex smooth Banach space. We apply these results to localize two nontrivial solutions for Dirichlet problems involving nonhomogeneous operators in the context of Orlicz–Sobolev spaces. As a special case, we obtain also the existence of two nontrivial positive solutions located on a certain ball for p-Laplacian boundary value problems.