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

Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Dušan D. Repovš

Published 2017-04-26Version 1

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 Carath\'eodory 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.