Nontrivial solutions for nonvariational quasilinear Neumann problems

Nikolaos S. Papageorgiou, Sandrina Rafaela Andrade Santos, Vasile Staicu

Abstract


We consider a nonlinear nonvariational Neumann problem with a nonsmooth
potential. Using the spectrum of the assymptotic (as $\vert x\vert
\rightarrow\infty)$ differential operator and degree theoretic techniques
based on the degree map of certain multivalued perturbations of
(S)$_{+}$-operators, we establish the existence of at least one
nontrivial smooth solution.

Keywords


Nonvariational problem; asymptotic differential operator; degree theory; (S)$_{+}$-operator; nonsmooth potential; generalized subdifferential

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