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.
Applied Mathematics and Computation – Elsevier
Published: Jul 15, 2018
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