Degree theoretic methods in the study of positive solutions for nonlinear hemivariational inequalities. (English) Zbl 1212.35081

Filippakis, Michael E.; Papageorgiou, Nikolaos S.

Differ. Integral Equ. 19, No. 2, 223-240 (2006).

Summary: In this paper we study the existence of positive solutions for nonlinear elliptic problems driven by the \(p\)-Laplacian and with a nonsmooth potential (hemivariational inequalities). The hypotheses, in the case \(p=2\) (semilinear problems), incorporate in our framework of analysis the so-called asymptotically linear problems. The approach is degree theoretic method based on the fixed-point index for nonconvex-valued multifunctions due to R. Bader [Z. Anal. Anwend. 20, No. 1, 3-15 (2001; Zbl 0985.34053)].

MSC:

35J20	Variational methods for second-order elliptic equations
35J60	Nonlinear elliptic equations
35R70	PDEs with multivalued right-hand sides
47H11	Degree theory for nonlinear operators

Keywords:

\(p\)-Laplacian; asymptotically linear problems; fixed-point index; nonconvex-valued multifunction

Citations:

Zbl 0985.34053