Kirchhoff type elliptic equations with double criticality in Musielak–Sobolev spaces
Shilpa Gupta, Gaurav Dwivedi
Abstract
This paper aims to establish the existence of a weak solution for the nonlocal problem: where is a bounded and smooth domain containing two open and connected subsets and such that and is the ‐Laplace operator. We assume that reduces to in and to in , the nonlinear function acts as on and as on for sufficiently large . To establish the existence results in a Musielak–Sobolev space, we use a variational technique based on the mountain pass theorem.
Topics & Concepts
MathematicsSobolev spaceMountain pass theoremBounded functionType (biology)Mountain passDomain (mathematical analysis)Mathematical analysisp-LaplacianNonlinear systemLaplace transformFunction spaceSpace (punctuation)Operator (biology)Pure mathematicsBoundary value problemBiochemistryPhysicsRepressorQuantum mechanicsBiologyTranscription factorChemistryGeneEcologyLinguisticsPhilosophyNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringStability and Controllability of Differential Equations