Nikolaos Socrates Papageorgiou (Author), Vicenţiu Rǎdulescu (Author), Dušan Repovš (Author)

Abstract

We consider a parametric semilinear Robin problem driven by the Laplacian plus an indefinite and unbounded potential. In the reaction, we have the competing effects of a concave term appearing with a negative sign and of an asymmetric asymptotically linear term which is resonant in the negative direction. Using variational methods together with truncation and perturbation techniques and Morse theory (critical groups), we prove two multiplicity theorems producing four and five, respectively, nontrivial smooth solutions when the parameter ▫$\lambda > 0$▫ is small.

Keywords

indefinite and unbounded potential;concave term;asymmetric reaction;critical groups;multiple solutions;Harnack inequality;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UL FMF - Faculty of Mathematics and Physics
UDC: 517.956.2
COBISS: 18385753 Link will open in a new window
ISSN: 1536-1365
Views: 530
Downloads: 381
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Other data

Type (COBISS): Article
Pages: str. 69-87
Volume: ǂVol. ǂ19
Issue: ǂiss. ǂ1
Chronology: Feb. 2019
DOI: 10.1515/ans-2018-2022
ID: 11191166