On a class of nonlinear variational-hemivariational inequalities. (English) Zbl 1149.35354
The authors deal with a three critical points theorem for a so-called variational-hemivariational inequality
\[
\Phi^0(u,v-u)+\Psi(v)-\Psi(u)\geq 0\quad\forall v\in X
\]
where \(X\) is a Banach space, \(\Phi\) a locally Lipschitz continuous function, \(\Psi\) a convex, proper and lower semicontinuous function, and \(\Phi^0(u,v)\) denotes the generalized directional derivative of \(\Phi\) at \(u\) along \(v\). They obtain existence of multiple solutions for a Neumann elliptic variational-hemivariational inequality involving the \(p\)-Laplacian. Moreover, they study a Neumann problem for elliptic equations with discontinuous nonlinearities.
Reviewer: Messoud A. Efendiev (Berlin)
MSC:
35J85 | Unilateral problems; variational inequalities (elliptic type) (MSC2000) |
35A15 | Variational methods applied to PDEs |
35J60 | Nonlinear elliptic equations |
35R05 | PDEs with low regular coefficients and/or low regular data |
47J20 | Variational and other types of inequalities involving nonlinear operators (general) |
49J40 | Variational inequalities |
Keywords:
variational-hemivariational inequality; \(p\)-Laplacian; Neumann problem; discontinuous nonlinearityReferences:
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