Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 43, 2018, 483-508

RESONANT ROBIN PROBLEMS DRIVEN BY THE p-LAPLACIAN PLUS AN INDEFINITE POTENTIAL

Nikolaos S. Papageorgiou, Vicentiu D. Radulescu and Dusan D. Repovs

National Technical University, Department of Mathematics
Zografou Campus, Athens 15780, Greece; npapg 'at' math.ntua.gr

AGH University of Science and Technology, Faculty of Applied Mathematics
al. Mickiewicza 30, 30-059 Krakow, Poland
and University of Craiova, Department of Mathematics
200585 Craiova, Romania; vicentiu.radulescu 'at' imar.ro

University of Ljubljana, Faculty of Education and Faculty of Mathematics and Physics
SI-1000 Ljubljana, Slovenia; dusan.repovs 'at' guest.arnes.si

Abstract. We consider a nonlinear Robin problems driven by the p-Laplacian plus an indefinite potential. The reaction is resonant with respect to a variational eigenvalue. For the principal eigenvalue we assume strong resonance. Using variational tools and critical groups we prove existence and multiplicity theorems.

2010 Mathematics Subject Classification: Primary 35J20, 35J60, 58E05.

Key words: p-Laplacian, indefinite potential, resonance, strong resonance, variational eigenvalue, nonlinear regularity, critical groups, Robin boundary condition.

Reference to this article: N. S. Papageorgiou, V. D. Radulescu and D. D. Repovs: Resonant Robin problems driven by the p-Laplacian plus an indefinite potential. Ann. Acad. Sci. Fenn. Math. 43 (2018), 483-508.

Full document as PDF file

https://doi.org/10.5186/aasfm.2018.4331