Hammerstein integral inclusions

in reflexive Banach spaces

Authors:
Tiziana Cardinali and Nikolaos S. Papageorgiou

Journal:
Proc. Amer. Math. Soc. **127** (1999), 95-103

MSC (1991):
Primary 47H04, 47H30, 45G10

DOI:
https://doi.org/10.1090/S0002-9939-99-04906-0

MathSciNet review:
1610932

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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:
https://doi.org/10.1090/S0002-9939-99-04906-0

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

Article copyright:
© Copyright 1999
American Mathematical Society