Existence and multiplicity of solutions for some Steklov problem involving (p₁(x), p₂(x))-Laplacian operator

ABSTRACT

In this paper, we study the existence and multiplicity of weak solutions to a $(p_1(x);p_2(x))$-Laplacian problem. By means of variational methods, mountain pass lemma and its $Z_2$ symmetric version, we establish the existence and multiplicity of solutions.

KEYWORDS:

• $p(x)$-Laplacian
• variational methods
• variable exponent Sobolev space

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 35J20
• 35J60
• 35G30
• 35J35

Disclosure statement

No potential conflict of interest was reported by the authors.

Data availability statement

No data were produced for this paper.