Search results for " Superlinear perturbation"

showing 2 items of 2 documents

Positive solutions for singular (p, 2)-equations

2019

We consider a nonlinear nonparametric Dirichlet problem driven by the sum of a p-Laplacian and of a Laplacian (a (p, 2)-equation) and a reaction which involves a singular term and a $$(p-1)$$ -superlinear perturbation. Using variational tools and suitable truncation and comparison techniques, we show that the problem has two positive smooth solutions.

Dirichlet problemApplied MathematicsGeneral Mathematics010102 general mathematicsNonparametric statisticsSingular termGeneral Physics and AstronomyPerturbation (astronomy)Mathematics::Spectral Theory01 natural sciences010101 applied mathematicsNonlinear systemSettore MAT/05 - Analisi MatematicaSingular term Superlinear perturbation Positive solution Nonlinear regularity Truncation Maximum principle Double phase problemApplied mathematics0101 mathematicsLaplace operatorMathematicsZeitschrift für angewandte Mathematik und Physik
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Perturbed eigenvalue problems for the Robin p-Laplacian plus an indefinite potential

2020

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.

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 principleAnalysis
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