Multiplicity results for a system involving the p(x)- Laplacian operator

Abstract

In this manuscript, it is considered existence and multiplicity of solutions for a system involving the -Laplacian operator which are related to several applications such as electrorheological fluids, image processing, robotics and space technology. A first solution for the system considered is obtained, under general conditions, by combining sub-supersolutions with a minimization argument in convex sets. Additionally, considering an Ambrosetti-Rabinowitz type condition and applying the Mountain Pass Theorem it is proved the existence of a second solution for the problem. The hypotheses allow to consider an wide class of nonlinearities and the results in this paper improve and complement some recent contributions.

Keywords:

• p(x)-Laplacian
• sub-supersolutions
• variable exponents
• existence
• multiplicity

2020 Mathematics Subject Classifications:

• 35J60
• 35J70

Disclosure statement

No potential conflict of interest was reported by the author(s).