期刊
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
卷 37, 期 5, 页码 2589-2618出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcds.2017111
关键词
Indefinite and unbounded potential; Robin eigenvalue problem; sublinear perturbation; superlinear perturbation; maximum principle; positive solution; minimal positive solution
资金
- Slovenian Research Agency [P1-0292-0101, J1-7025-0101, J1-6721-0101]
- Romanian National Authority for Scientific Research UEFISCDI [PCCA-23/2014]
We study perturbations of the eigenvalue problem for the negative Laplacian plus an indefinite and unbounded potential and Robin boundary condition. First we consider the case of a sublinear perturbation and then of a superlinear perturbation. For the first case we show that for lambda < <(lambda(1))over cap> ((lambda(1)) over cap being the principal eigenvalue) there is one positive solution which is unique under additional conditions on the perturbation term. For lambda > (lambda(1)) over cap there are no positive solutions. In the superlinear case, for A < Al we have at least two positive solutions and for lambda >= <(lambda(1))over cap> there are no positive solutions. For both cases we establish the existence of a minimal positive solution (u) over bar (lambda) and we investigate the properties of the map lambda bar right arrow (u) over bar (lambda).
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