Existence and multiplicity of solutions for resonant nonlinear Neumann problems - Aizicovici, Sergiu; Papageorgiou, Nikolaos S.; Staicu, Vasile (Topological Methods in Nonlinear Analysis, 2010)
We consider nonlinear Neumann problems driven by the $p$-Laplaciandifferential operator with a Caratheodory nonlinearity. Under hypotheses whichallow resonance with respect to the principal eigenvalue $λ_{0}$ $=0$ at$±∞$, we prove existence and multiplicity results. Our approach isvariational and uses critical point theory and Morse theory (critical groups).