Nonlinear hemivariational inequalities of second order using the method of upper-lower solutions

Authors:
Nikolaos C. Kourogenis and Nikolaos S. Papageorgiou

Journal:
Proc. Amer. Math. Soc. **131** (2003), 2359-2369

MSC (2000):
Primary 35J50, 35J85, 35R70

DOI:
https://doi.org/10.1090/S0002-9939-03-06993-4

Published electronically:
March 11, 2003

MathSciNet review:
1974632

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we examine a nonlinear hemivariational inequality of second order. The differential operator is set-valued, nonlinear and depends on both and its gradient . The same is true for the zero order term , while the right-hand side nonlinearity satisfies a one-sided Lipschitz condition. We use the method of upper and lower solutions, coupled with truncation and penalization techniques and the fixed point theory for multifunctions in an ordered Banach space.

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Additional Information

**Nikolaos C. Kourogenis**

Affiliation:
Department of Mathematics, National Technical University, Zografou Campus, Athens 157 80, Greece

Address at time of publication:
Department of Financial Management and Banking, University of Pireus, Pireus, Greece

**Nikolaos S. Papageorgiou**

Affiliation:
Department of Mathematics, National Technical University, Zografou Campus, Athens 157 80, Greece

Email:
npapg@math.ntua.gr

DOI:
https://doi.org/10.1090/S0002-9939-03-06993-4

Keywords:
Upper solution,
lower solution,
upper semicontinuous multifunction,
lower semicontinuous multifunction,
graph measurability,
operator of type $S_+ $,
pseudomonotone operator,
truncation map,
penalty map,
coercive map,
order interval

Received by editor(s):
October 9, 2001

Published electronically:
March 11, 2003

Additional Notes:
The first author was supported by a grant of the National Scholarship Foundation of Greece (I.K.Y.)

Communicated by:
David S. Tartakoff

Article copyright:
© Copyright 2003
American Mathematical Society