On double phase Kirchhoff problems with singular nonlinearity
Rakesh Arora, Alessio Fiscella, Tuhina Mukherjee, Patrick Winkert
Abstract
Abstract In this paper, we study multiplicity results for double phase problems of Kirchhoff type with right-hand sides that include a parametric singular term and a nonlinear term of subcritical growth. Under very general assumptions on the data, we prove the existence of at least two weak solutions that have different energy sign. Our treatment is based on the fibering method in form of the Nehari manifold. We point out that we cover both the nondegenerate as well as the degenerate Kirchhoff case in our setting.
Topics & Concepts
Nehari manifoldMultiplicity (mathematics)MathematicsNonlinear systemDegenerate energy levelsMathematical analysisParametric statisticsTerm (time)Manifold (fluid mechanics)Cover (algebra)Pure mathematicsPhysicsQuantum mechanicsStatisticsMechanical engineeringEngineeringNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringStability and Controllability of Differential Equations