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Nonlinear hemivariational inequalities of second order using the method of upper-lower solutions
Author(s):
Nikolaos
C.
Kourogenis;
Nikolaos
S.
Papageorgiou
Journal:
Proc. Amer. Math. Soc.
131
(2003),
2359-2369.
MSC (2000):
Primary 35J50, 35J85, 35R70
Posted:
March 11, 2003
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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:
10.1090/S0002-9939-03-06993-4
PII:
S 0002-9939(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
Posted:
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
Copyright of article:
Copyright
2003,
American Mathematical Society
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