### Existence and multiplicity of solutions for resonant nonlinear Neumann problems

#### 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).

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).

#### Keywords

Resonant problems; homological local linking; linking sets; Neumann p-Laplacian

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