Localization method for the solutions of nonhomogeneous operator equations

Hannelore Lisei, Csaba Varga and Orsolya Vas

Applied Mathematics and Computation, 2018, vol. 329, issue C, 64-83

Abstract: 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.

Keywords: Critical point theory; Mountain pass theorem; Orlicz–Sobolev space; Nonhomogeneous operator equation (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:329:y:2018:i:c:p:64-83

DOI: 10.1016/j.amc.2018.01.031

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