Generalized critical Kirchhoff-type potential systems with Neumann Boundary conditions
Nabil Chems Eddine, Maria Alessandra Ragusa
Abstract
In this paper, we consider a class of quasilinear stationary Kirchhoff type potential systems with Neumann Boundary conditions, which involves a general variable exponent elliptic operator with critical growth. Under some suitable conditions on the nonlinearities, we establish existence and multiplicity of solutions for the problem by using the concentration-compactness principle of Lions for variable exponents and the mountain pass theorem without the Palais–Smale condition.
Topics & Concepts
MathematicsNeumann boundary conditionMathematical analysisBoundary value problemMultiplicity (mathematics)Type (biology)Operator (biology)Critical exponentMountain pass theoremBoundary (topology)Variable (mathematics)Class (philosophy)Pure mathematicsNonlinear systemScalingGeometryPhysicsBiochemistryEcologyRepressorChemistryQuantum mechanicsBiologyTranscription factorArtificial intelligenceComputer scienceGeneNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringStability and Controllability of Differential Equations