Differential and Integral Equations

Degree theoretic methods in the study of positive solutions for nonlinear hemivariational inequalities

Michael E. Filippakis and Nikolaos S. Papageorgiou

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Abstract

In this paper we study the existence of positive solutions for nonlinear elliptic problems driven by the $p$-Laplacian differential operator 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 based on the fixed-point index for nonconvex-valued multifunctions due to Bader [3].

Article information

Source
Differential Integral Equations, Volume 19, Number 2 (2006), 223-240.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356050526

Mathematical Reviews number (MathSciNet)
MR2194505

Zentralblatt MATH identifier
1212.35081

Subjects
Primary: 35J85
Secondary: 35J20: Variational methods for second-order elliptic equations 35J60: Nonlinear elliptic equations 35R70: Partial differential equations with multivalued right-hand sides 47H11: Degree theory [See also 55M25, 58C30] 47J20: Variational and other types of inequalities involving nonlinear operators (general) [See also 49J40]

Citation

Filippakis, Michael E.; Papageorgiou, Nikolaos S. Degree theoretic methods in the study of positive solutions for nonlinear hemivariational inequalities. Differential Integral Equations 19 (2006), no. 2, 223--240. https://projecteuclid.org/euclid.die/1356050526


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