Ground state and nodal solutions for a class of double phase problems
Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Dušan Repovš
Abstract
We consider a double phase problem driven by the sum of the p-Laplace operator and a weighted q-Laplacian ($$q<p$$), with a weight function which is not bounded away from zero. The reaction term is $$(p-1)$$-superlinear. Employing the Nehari method, we show that the equation has a ground state solution of constant sign and a nodal (sign-changing) solution.
Topics & Concepts
Sign (mathematics)Laplace operatorMathematicsNehari manifoldConstant (computer programming)Bounded functionGround stateLaplace transformMathematical analysisFunction (biology)Operator (biology)Phase (matter)Class (philosophy)Zero (linguistics)Pure mathematicsMathematical physicsPhysicsQuantum mechanicsNonlinear systemChemistryComputer scienceEvolutionary biologyGenePhilosophyTranscription factorProgramming languageLinguisticsArtificial intelligenceRepressorBiologyBiochemistryNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringSpectral Theory in Mathematical Physics