Multiple solutions for parametric double phase Dirichlet problems
Nikolas S. Papageorgiou, Calogero Vetro, Francesca Vetro
Abstract
We consider a parametric double phase Dirichlet problem. Using variational tools together with suitable truncation and comparison techniques, we show that for all parametric values [Formula: see text] the problem has at least three nontrivial solutions, two of which have constant sign. Also, we identify the critical parameter [Formula: see text] precisely in terms of the spectrum of the [Formula: see text]-Laplacian.
Topics & Concepts
MathematicsDirichlet problemTruncation (statistics)Parametric statisticsConstant (computer programming)Sign (mathematics)Applied mathematicsDirichlet distributionSpectrum (functional analysis)Mathematical analysisPure mathematicsCombinatoricsBoundary value problemStatisticsComputer scienceQuantum mechanicsPhysicsProgramming languageNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringNonlinear Differential Equations Analysis