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

Abstract

We consider a nonlinear, nonhomogeneous Robin problem with an indefinite potential and a nonsmooth primitive in the reaction term. In fact, the right-hand side of the problem (reaction term) is the Clarke subdifferential of a locally Lipschitz integrand. We assume that asymptotically this term is resonant with respect the principal eigenvalue (from the left). We prove the existence of three nontrivial smooth solutions, two of constant sign and the third nodal. We also show the existence of extremal constant sign solutions. The tools come from nonsmooth critical point theory and from global optimization (direct method).

Keywords

locally Lipschitz function;Clarke subdifferential;resonance;extremal constant sign solutions,;nodal solutions;nonlinear nonhomogeneous differential operator;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UL FMF - Faculty of Mathematics and Physics
UDC: 517.956
COBISS: 18130265 Link will open in a new window
ISSN: 0022-3239
Views: 432
Downloads: 394
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Other data

Type (COBISS): Article
Pages: str. 293-323
Volume: ǂVol. ǂ175
Issue: ǂiss. ǂ2
Chronology: Nov. 2017
DOI: 10.1007/s10957-017-1173-5
ID: 11221927