SOLUTION FOR STEKLOV BOUNDARY VALUE PROBLEM INVOLVING THE P(X)- LAPLACIAN OPERATORS

Abstract

In this paper, we concerned with Steklov boundary value problem involving - Laplacian operator. By means of the Mountain Pass theorem together with Ambrosetti- Rabinowitz condition, we prove the existence nontrivial weak of solutions in Sobolev spaces with variable exponent under appropriate conditions on f(x,u) .

Keywords

• Variable exponent Lebesgue-Sobolev spaces
• variational methods
• Ambrosetti- Rabinowitz condition

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