Existence results for double phase implicit obstacle problems involving multivalued operators
Shengda Zeng, Yunru Bai, Leszek Gasiński, Patrick Winkert
Abstract
Abstract In this paper we study implicit obstacle problems driven by a nonhomogenous differential operator, called double phase operator, and a multivalued term which is described by Clarke’s generalized gradient. Based on a surjectivity theorem for multivalued mappings, Kluge’s fixed point principle and tools from nonsmooth analysis, we prove the existence of at least one solution.
Topics & Concepts
MathematicsOperator (biology)ObstacleTerm (time)Differential operatorPure mathematicsFixed pointObstacle problemFixed-point theoremMathematical analysisApplied mathematicsVariational inequalityPhysicsLawPolitical scienceChemistryQuantum mechanicsTranscription factorRepressorGeneBiochemistryNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringContact Mechanics and Variational Inequalities