Existence Results for Steklov Problem With Nonlinear Boundary Condition

Abstract

In this article, we study the nonlinear Steklov boundary value problem. The existence of a nontrivial weak solution is obtained on variable exponent Sobolev spaces, by means of the Mountain Pass theorem.

Infinitely many solutions for a p(x)-Kirchhoff type equation with Steklov boundary value

“…The Steklov problems involving p (x)-Laplacian have been worked by some of the authors [15,22,24]. Especially, the authors have studied the problems of type (E) when M(t) = 1.…”