Two solutions for Dirichlet double phase problems with variable exponents

Abstract

This paper is devoted to the study of a double phase problem with variable exponents and Dirichlet boundary condition. Based on an abstract critical point theorem, we establish existence results under very general assumptions on the nonlinear term, such as a subcritical growth and a superlinear condition. In particular, we prove the existence of two bounded weak solutions with opposite energy sign and we state some special cases in which they turn out to be nonnegative.

Keywords

• bounded solutions
• critical point theory
• double phase operator with variable exponents
• multiplicity results
• superlinear reaction
• 35a01
• 35b33
• 35d30
• 35j62
• 35j66