Abstract
We consider a nonlinear periodic problem driven by the scalar p-Laplacian, with an asymptotically (p−1)-linear nonlinearity. We permit resonance with respect to the second positive eigenvalue of the negative periodic scalar p-Laplacian and we assume nonuniform nonresonance with respect to the first positive eigenvalue. Using a combination of variational methods, with truncation techniques and Morse theory, we show that the problem has at least three nontrivial solutions.
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Motreanu, D., Motreanu, V.V. & Papageorgiou, N.S. Multiple solutions for resonant nonlinear periodic equations. Nonlinear Differ. Equ. Appl. 17, 535–557 (2010). https://doi.org/10.1007/s00030-010-0067-0
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DOI: https://doi.org/10.1007/s00030-010-0067-0