Abstract
We consider nonlinear Neumann problems driven by the $p$-Laplacian differential operator with a Caratheodory nonlinearity. Under hypotheses which allow resonance with respect to the principal eigenvalue $\lambda_{0}=0$ at $\pm\infty$, we prove existence and multiplicity results. Our approach is variational and uses critical point theory and Morse theory (critical groups).
Citation
Sergiu Aizicovici. Nikolaos S. Papageorgiou. Vasile Staicu. "Existence and multiplicity of solutions for resonant nonlinear Neumann problems." Topol. Methods Nonlinear Anal. 35 (2) 235 - 252, 2010.
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