Nonlinear Dirichlet problems with unilateral growth on the reaction
ID Papageorgiou, Nikolaos S. (Author), ID Rǎdulescu, Vicenţiu (Author), ID Repovš, Dušan (Author)

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We consider a nonlinear Dirichlet problem driven by the ▫$p$▫-Laplace differential operator with a reaction which has a subcritical growth restriction only from above. We prove two multiplicity theorems producing three nontrivial solutions, two of constant sign and the third nodal. The two multiplicity theorems differ on the geometry near the origin. In the semilinear case (that is, ▫$p=2$▫), using Morse theory (critical groups), we produce a second nodal solution for a total of four nontrivial solutions. As an illustration, we show that our results incorporate and significantly extend the multiplicity results existing for a class of parametric, coercive Dirichlet problems

Keywords:unilateral growth, constant sign and nodal solutions, multiplicity theorems, critical groups
Work type:Article
Typology:1.01 - Original Scientific Article
Organization:PEF - Faculty of Education
FMF - Faculty of Mathematics and Physics
Number of pages:Str. 319-340
Numbering:Vol. 31, iss. 2
PID:20.500.12556/RUL-108788 This link opens in a new window
ISSN on article:0933-7741
DOI:10.1515/forum-2018-0114 This link opens in a new window
COBISS.SI-ID:18471257 This link opens in a new window
Publication date in RUL:25.07.2019
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Title:Forum mathematicum
Shortened title:Forum math.
Publisher:de Gruyter
COBISS.SI-ID:26801408 This link opens in a new window

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