Existence of solutions for p(x)-Kirchhoff type problems with non-smooth potentials

Abstract

We consider a class of p(x)-Kirchhoff type problem with a subdifferential term and a discontinuous perturbation. Assuming the existence of an ordered pair of appropriately defined upper and lower solutions, by the method of lower-upper solutions, penalization techniques, truncations, and results from nonlinear and multivalued analysis, we show the existence of solutions, and of extremal solutions in the interval defined by the lower and upper solution.

Keywords

• Extremal solutions
• fixed point
• p(x)-Kirchhoff type problem
• upper and lower solutions