We consider nonlinear elliptic Neumann problems driven by the p-Laplacian. Using variational techniques together with Morse theory (in particular, critical groups and the Poincaré-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.
- Morse theory
- Multiple solutions.
- Neumann problem
ASJC Scopus subject areas
- Statistical and Nonlinear Physics