Perturbed eigenvalue problems for the Robin p-Laplacian plus an indefinite potential

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Abstract

We consider a parametric nonlinear Robin problem driven by the negative p-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, ·) is (p- 1) -sublinear and then the case where it is (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 λ∈ R which we specify exactly in terms of principal eigenvalue of the differential operator.
Lingua originaleEnglish
pagine (da-a)1-34
Numero di pagine34
RivistaAnalysis and Mathematical Physics
Volume10
Stato di pubblicazionePublished - 2020

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Mathematical Physics

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