Two solutions for Dirichlet double phase problems with variable exponents
Eleonora Amoroso, Gabriele Bonanno, Giuseppina D’Aguì, Patrick Winkert
Abstract
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.
Topics & Concepts
MathematicsDirichlet boundary conditionBounded functionSign (mathematics)Nonlinear systemDirichlet problemVariable (mathematics)Dirichlet distributionMathematical analysisCritical point (mathematics)Term (time)Boundary (topology)Pure mathematicsBoundary value problemApplied mathematicsPhysicsQuantum mechanicsNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringNonlinear Differential Equations Analysis