Existence of solutions for singular double phase problems via the Nehari manifold method
Wulong Liu, Guowei Dai, Nikolaos S. Papageorgiou, Patrick Winkert
Abstract
Abstract In this paper we study quasilinear elliptic equations driven by the double phase operator and a right-hand side which has the combined effect of a singular and of a parametric term. Based on the fibering method by using the Nehari manifold we are going to prove the existence of at least two weak solutions for such problems when the parameter is sufficiently small.
Topics & Concepts
Nehari manifoldMathematicsMathematical analysisOperator (biology)Manifold (fluid mechanics)Pure mathematicsParametric statisticsPhase (matter)Term (time)Applied mathematicsPhysicsNonlinear systemQuantum mechanicsBiochemistryChemistryEngineeringTranscription factorStatisticsGeneRepressorMechanical engineeringNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringAdvanced Mathematical Physics Problems