Multiple solutions for resonant nonlinear periodic equations

作者：Motreanu D^*; Motreanu V V; Papageorgiou N S

来源：Nodea-Nonlinear Differential Equations and Applications, 2010, 17(5): 535-557.

DOI：10.1007/s00030-010-0067-0

• Scalar p-Laplacian
• Morse theory
• Resonant problem
• Truncation
• Solutions of constant sign
• Homotopy

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.

• 出版日期2010-10