Non-smooth extension of a three critical points theorem by Ricceri with an application to p(x)-Laplacian differential inclusions

Abstract

We extend a smooth Ricceri three critical-points theorem to a non-smooth case. Our approach is based on the non-smooth analysis. As an application, we obtain the existence of at least three critical points for a p(x)-Laplacian differential inclusion.

Keywords

• Nonsmooth critical point theory
• locally Lipschitz
• differential inclusion
• p(x)-Laplacian