Asymmetric Robin problems with indefinite potential and concave terms
ID Papageorgiou, Nikolaos S. (Author), ID Rǎdulescu, Vicenţiu (Author), ID Repovš, Dušan (Author)

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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
Work type:Article
Typology:1.01 - Original Scientific Article
Organization:PEF - Faculty of Education
FMF - Faculty of Mathematics and Physics
Number of pages:Str. 69-87
Numbering:Vol. 19, iss. 1
PID:20.500.12556/RUL-108743 This link opens in a new window
ISSN on article:1536-1365
DOI:10.1515/ans-2018-2022 This link opens in a new window
COBISS.SI-ID:18385753 This link opens in a new window
Publication date in RUL:17.07.2019
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Record is a part of a journal

Title:Advanced nonlinear studies
Shortened title:Adv. nonlinear stud.
Publisher:De Gruyter
COBISS.SI-ID:15060569 This link opens in a new window

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