POSITIVE WEAK SOLUTIONS OF THE STEKLOV PROBLEM FOR A CLASS OF QUASI LINEAR ELLIPTIC OPERATORS CONTAINING THE p(·)- LAPLACIAN AND THE MEAN CURVATURE OPERATOR

Abstract

In this paper, we consider the existence of positive weak solutions for a class of quasilinear elliptic operators containing p(·)-Laplacian and mean curvature operator with the Steklov boundary condition. The results for p(·)-Laplacian are known, however, we attempt in this paper to extend the results for a class of quasilinear elliptic operators containing not only p(·)-Laplacian but also the mean curvature operator.