THe Existence of two solutions for $(p(x),q(x))$-Laplacian problems with Steklov boundary conditions

The present paper discusses an elliptic equation with Steklov boundary conditions and $(p(x),q(x))$-Laplacian. Using mountain pass theorem together with Ekeland's variational principle, we prove, under appropriate conditions on the functions involved, that the problem admits at least two solutions.