Three solutions for a partial discrete Dirichlet boundary value problem with p-Laplacian
Shaohong Wang, Zhan Zhou
Abstract
Abstract By employing critical point theory, we investigate the existence of solutions to a boundary value problem for a p -Laplacian partial difference equation depending on a real parameter. To be specific, we give precise estimates of the parameter to guarantee that the considered problem possesses at least three solutions. Furthermore, based on a strong maximum principle, we show that two of the obtained solutions are positive under some suitable assumptions of the nonlinearity.
Topics & Concepts
MathematicsPartial differential equationBoundary value problemDirichlet distributionMathematical analysisDirichlet problemOrdinary differential equationElliptic boundary value problemNonlinear systemDirichlet boundary conditionApplied mathematicsp-LaplacianValue (mathematics)Laplace operatorBoundary (topology)Free boundary problemDifferential equationPhysicsStatisticsQuantum mechanicsNonlinear Differential Equations AnalysisNonlinear Partial Differential EquationsStability and Controllability of Differential Equations