6533b85dfe1ef96bd12bdf3c
RESEARCH PRODUCT
Perturbed eigenvalue problems for the Robin p-Laplacian plus an indefinite potential
Calogero Vetrosubject
Pure mathematicsSublinear functionPerturbation (astronomy)Sublinear and superlinear perturbationLambda01 natural sciencesNonlinear Picone’s identitySettore MAT/05 - Analisi MatematicaUniqueness0101 mathematicsMathematical PhysicsEigenvalues and eigenvectorsPositive solutionsMathematicsNonlinear regularityAlgebra and Number TheoryMinimal positive solution010102 general mathematicsDifferential operator010101 applied mathematicsNonlinear systemp-LaplacianIndefinite potentialUniquenessNonlinear maximum principleAnalysisdescription
AbstractWe consider a parametric nonlinear Robin problem driven by the negativep-Laplacian plus an indefinite potential. The equation can be thought as a perturbation of the usual eigenvalue problem. We consider the case where the perturbation$$f(z,\cdot )$$f(z,·)is$$(p-1)$$(p-1)-sublinear and then the case where it is$$(p-1)$$(p-1)-superlinear but without satisfying the Ambrosetti–Rabinowitz condition. We establish existence and uniqueness or multiplicity of positive solutions for certain admissible range for the parameter$$\lambda \in {\mathbb {R}}$$λ∈Rwhich we specify exactly in terms of principal eigenvalue of the differential operator.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2020-11-01 |