Multiple Nontrivial Solutions for Neumann Problems Involving the p-Laplacian: a Morse Theoretical Approach

作者：Kristaly Alexandru^*; Papageorgiou Nikolaos S

来源：Advanced Nonlinear Studies, 2010, 10(1): 83-107.

• Neumann problem
• p-Laplacian
• Morse theory
• multiple solutions

We consider nonlinear elliptic Neumann problems driven by the p-Laplacian. Using variational techniques together with Morse theory (in particular, critical groups and the Poincare-Hopf formula), we prove some multiplicity results: either three or four distinct nontrivial solutions are guaranteed, depending on the geometry and smoothness of the nonlinear term.

• 出版日期2010-2