Nonhomogeneous hemivariational inequalities with indefinite potential and Robin boundary condition

Papageorgiou, Nikolaos S. (author), Rǎdulescu, Vicenţiu (author), Repovš, Dušan (author)

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).

• Language: English
• Keywords: locally Lipschitz function, Clarke subdifferential, resonance, extremal constant sign solutions, nodal solutions, nonlinear nonhomogeneous differential operator
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Year: 2017
• Number of pages: Str. 293-323
• Numbering: Vol. 175, iss. 2
• PID: 20.500.12556/RUL-110112
• UDC: 517.956
• ISSN on article: 0022-3239
• DOI: 10.1007/s10957-017-1173-5
• COBISS.SI-ID: 18130265
• Publication date in RUL: 12.09.2019