Variational approach for a Steklov problem involving nonstandard growth conditions

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.