Multiple solutions for resonant hemivariational inequalities via minimax methods. (English) Zbl 1182.35095
Authors’ abstract: We consider nonlinear Dirichlet problems driven by the \(p\)-Laplacian differential operator with a nonsmooth potential (hemivariational inequalities). We assume that the problem is resonant at infinity with respect to \(\lambda_1>0\) (the principal eigenvalue of the Dirichlet \(p-\)Laplacian) from the right. Using minimax methods based on the nonsmooth critical point theory we prove an existence and a multiplicity theorem.
Reviewer: Huansong Zhou (Wuhan)
MSC:
| 35J25 | Boundary value problems for second-order elliptic equations |
| 35J20 | Variational methods for second-order elliptic equations |
| 35J92 | Quasilinear elliptic equations with \(p\)-Laplacian |
| 35J87 | Unilateral problems for nonlinear elliptic equations and variational inequalities with nonlinear elliptic operators |
| 49J40 | Variational inequalities |
Keywords:
hemivariational inequalities; nonsmooth critical points; resonance; nonsmooth potential; linking setReferences:
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