Nonlinear resonant problems with an indefinite potential and concave boundary condition
- Resource Type
- article
- Authors
- Nikolaos Papageorgiou; Andrea Scapellato
- Source
- Electronic Journal of Qualitative Theory of Differential Equations, Vol 2020, Iss 51, Pp 1-16 (2020)
- Subject
- resonant reaction
concave boundary term
critical group
nonlinear regularity
multiple solutions
Mathematics
QA1-939
- Language
- English
- ISSN
- 1417-3875
We consider a nonlinear elliptic problem driven by the $p$-Laplacian plus and indefinite potential term. The reaction is $(p-1)$-linear and resonant and the boundary term is concave. The problem is nonparametric. Using variational tools, together with truncation and perturbation techniques and critical groups, we show that the problem has at least three nontrivial smooth solutions.