Multiple solutions for resonant problems of the Robin ▫$p$▫-Laplacian plus an indefinite potential

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

We study a nonlinear boundary value problem driven by the ▫$p$▫-Laplacian plus an indefinite potential with Robin boundary condition. The reaction term is a Carathéodory function which is asymptotically resonant at ▫$\pm \infty$▫ with respect to a nonprincipal Ljusternik-Schnirelmann eigenvalue. Using variational methods, together with Morse theory and truncation-perturbation techniques, we show that the problem has at least three nontrivial smooth solutions, two of which have a fixed sign.

• Language: English
• Keywords: p-Laplacian, Robin boundary condition, resonance, critical groups, multiple nontrivial smooth solutions, indefinite potential
• 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: art. 63 [23 str.]
• Numbering: Vol. 56, iss. 3
• PID: 20.500.12556/RUL-110020
• UDC: 517.956.2
• ISSN on article: 0944-2669
• DOI: http://dx.doi.org/10.1007/s00526-017-1164-2
• COBISS.SI-ID: 18019929
• Publication date in RUL: 11.09.2019

Record is a part of a journal

• Title: Calculus of variations and partial differential equations
• Shortened title: Calc. var. partial differ. equ.
• Publisher: Springer
• ISSN: 0944-2669
• COBISS.SI-ID: 3677529