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

被引：1

作者：

Vetro, Calogero ^{[1
]}

机构：

[1] Univ Palermo, Dept Math & Comp Sci, Via Archirafi 34, I-90123 Palermo, Italy

来源：

ANALYSIS AND MATHEMATICAL PHYSICS | 2020年 / 10卷 / 04期

关键词：

Positive solutions; Sublinear and superlinear perturbation; Nonlinear Picone's identity; Nonlinear maximum principle; Nonlinear regularity; Indefinite potential; Minimal positive solution; Uniqueness; POSITIVE SOLUTIONS; NEUMANN PROBLEMS; NODAL SOLUTIONS; EQUATIONS; SIGN;

D O I：

10.1007/s13324-020-00416-w

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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, center dot) 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 lambda is an element of R which we specify exactly in terms of principal eigenvalue of the differential operator.

引用

页数：34

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