Multiplicity of solutions for non-homogeneous Neumann problems in Orlicz-Sobolev spaces

Date

2017-09-13

Authors

Heidarkhani, Shapour
Ferrara, Massimiliano
Caristi, Giuseppe
Henderson, Johnny
Salari, Amjad

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

This article concerns the existence of non-trivial weak solutions for a class of non-homogeneous Neumann problems. The approach is through variational methods and critical point theory in Orlicz-Sobolev spaces. We investigate the existence of two solutions for the problem under some algebraic conditions with the classical Ambrosetti-Rabinowitz condition on the nonlinear term and using a consequence of the local minimum theorem due to Bonanno and mountain pass theorem. Furthermore, by combining two algebraic conditions on the nonlinear term and employing two consequences of the local minimum theorem due Bonanno we ensure the existence of two solutions, by applying the mountain pass theorem of Pucci and Serrin, we set up the existence of the third solution for the problem.

Description

Keywords

Multiplicity results, Weak solution, Orlicz-Sobolev space, Non-homogeneous Neumann problem, Variational methods, Critical point theory

Citation

Heidarkhani, S., Ferrara, M., Caristi, G., Henderson, J., & Salari, A. (2017). Multiplicity of solutions for non-homogeneous Neumann problems in Orlicz-Sobolev spaces. <i>Electronic Journal of Differential Equations, 2017</i>(215), pp. 1-23.

Rights

Attribution 4.0 International

Rights Holder

Rights License