Variational approach for a Steklov problem involving nonstandard growth conditions

Abstract

The aim of this paper is to study the multiplicity of solutions for a nonlocal p(x)-Kirchhoff type problem with Steklov boundary value in variable exponent Sobolev spaces. We prove the existence of at least three solutions and a nontrivial weak solution of the problem, using the Ricceri's three critical points theorem together with Mountain Pass theorem.

Keywords

• variational methods
• p(x)-kirchhoff type equation
• steklov boundary value
• ricceri's critical points theorem
• weak solution