Multiple solutions with sign information for double‐phase problems with unbalanced growth
Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Wen Zhang
Abstract
Abstract We consider a double‐phase Dirichlet problem with unbalanced growth and a reaction term which is ‐sublinear and has partial interaction with the first eigenvalue of the weighted differential operator (nonuniform nonresonance). Using the Nehari method, we show that the problem has at least three nontrivial bounded solutions, positive, negative and nodal (sign‐changing). This paper extends and complements the main results in the recent paper Papageorgiou–Pudelko–Rădulescu ( Math. Annalen 385 (2023) 1707–1745).
Topics & Concepts
MathematicsSublinear functionSign (mathematics)Eigenvalues and eigenvectorsBounded functionOperator (biology)Mathematical analysisTerm (time)Dirichlet problemPure mathematicsApplied mathematicsBoundary value problemQuantum mechanicsGeneBiochemistryChemistryTranscription factorRepressorPhysicsAdvanced Mathematical Modeling in EngineeringNonlinear Partial Differential EquationsNonlinear Differential Equations Analysis