Nonlinear elliptic problems involving the generalized p(u)-Laplacian operator with Fourier boundary condition

Abstract

This paper considers the existence of entropy solutions for some generalized elliptic p(u)-Laplacian problem with Fourier boundary conditions, when the variable exponent p is a real continuous function and we have dependency on the solution u. We get the results by assuming the right-hand side function f to be an integrable function, and by using the regularization approach combined with the theory of Sobolev spaces with variable exponents.