Existence and multiplicity of solutions for double‐phase Robin problems
Νικόλαος Παπαγεωργίου, Vicenţiu D. Rădulescu, Dušan Repovš
Abstract
We consider a double phase Robin problem with a Carathéodory nonlinearity. When the reaction is superlinear but without satisfying the Ambrosetti–Rabinowitz condition, we prove an existence theorem. When the reaction is resonant, we prove a multiplicity theorem. Our approach is Morse theoretic, using the notion of homological local linking.
Topics & Concepts
MathematicsMultiplicity (mathematics)Morse codeMorse theoryNonlinear systemPure mathematicsApplied mathematicsMathematical analysisQuantum mechanicsElectrical engineeringEngineeringPhysicsNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringNonlinear Differential Equations Analysis