Nehari manifold approach for superlinear double phase problems with variable exponents
Ángel Crespo‐Blanco, Patrick Winkert
Abstract
Abstract In this paper we consider quasilinear elliptic equations driven by the variable exponent double phase operator with superlinear right-hand sides. Under very general assumptions on the nonlinearity, we prove a multiplicity result for such problems whereby we show the existence of a positive solution, a negative one and a solution with changing sign. The sign-changing solution is obtained via the Nehari manifold approach and, in addition, we can also give information on its nodal domains.
Topics & Concepts
Nehari manifoldMathematicsMultiplicity (mathematics)Sign (mathematics)ExponentNonlinear systemMathematical analysisManifold (fluid mechanics)Pure mathematicsCritical exponentVariable (mathematics)Operator (biology)PhysicsGeometryQuantum mechanicsScalingTranscription factorEngineeringMechanical engineeringGeneLinguisticsBiochemistryPhilosophyChemistryRepressorNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringDifferential Equations and Boundary Problems