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Hammerstein integral inclusions in reflexive Banach spaces
Author(s):
Tiziana
Cardinali;
Nikolaos
S.
Papageorgiou
Journal:
Proc. Amer. Math. Soc.
127
(1999),
95-103.
MSC (1991):
Primary 47H04, 47H30, 45G10
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Abstract:
In this paper we examine multivalued Hammerstein integral equations defined in a separable reflexive Banach space. We prove existence theorems for both the ``convex'' problem (the multifunction is convex-valued) and the ``nonconvex'' problem (the multifunction is not necessarily convex-valued). We also show that the solution set of the latter is dense in the solution set of the former (relaxation theorem). Finally we present some examples illustrating the applicability of our abstract results.
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Additional Information:
Tiziana
Cardinali
Affiliation:
Department of Mathematics, University of Perugia, Via Vanvitelli 1, Perugia 06123, Italy
Nikolaos
S.
Papageorgiou
Affiliation:
Department of Mathematics, National Technical University, Zografou Campus, Athens 157 80, Greece
Email:
npapg@math.ntua.gr
DOI:
10.1090/S0002-9939-99-04906-0
PII:
S 0002-9939(99)04906-0
Keywords:
Compact operator,
measurable multifunction,
lsc and usc multifunction,
multivalued Nemitsky operator,
$h$-continuous multifunction,
Leray-Schauder alternative theorem,
relaxation theorem,
elliptic inclusions,
Green's operator.
Received by editor(s):
March 6, 1997
Communicated by:
Palle E. T. Jorgensen
Copyright of article:
Copyright
1999,
American Mathematical Society
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