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arXiv · 1704.08001

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

Nikolaos S. Papageorgiou·Vicenţiu D. Rădulescu·Dušan D. Repovš
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Abstract

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.

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Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Dušan D. Repovš. 2017-04-26. Multiple solutions for resonant problems of the Robin $p$-Laplacian plus an indefinite potential. https://doi.org/10.1007/s00526-017-1164-2

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