Hammerstein integral inclusions in reflexive Banach spaces
Authors:
Tiziana Cardinali and Nikolaos S. Papageorgiou
Journal:
Proc. Amer. Math. Soc. 127 (1999), 95103
MSC (1991):
Primary 47H04, 47H30, 45G10
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 convexvalued) and the ``nonconvex'' problem (the multifunction is not necessarily convexvalued). 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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 H. Amann, Existence theorems for equations of Hammerstein type, Appl. Anal. 1 (1972), pp. 385397. MR 52:15142
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 A. Bressan and G. Colombo, Extensions and selections of maps with decomposable values, Studia Math. 90 (1988), pp. 6985. MR 89j:54021
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 H. Brezis and F. Browder, Existence theorems for nonlinear integral equations of Hammerstein and Urysohn type, Bull. AMS 81 (19750, pp. 7378. MR 53:11441
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 F. Browder, Nonlinear functional analysis and nonlinear integral equations of Hammerstein and Urysohn type in Contributions to Nonlinear Functional Analysis, ed. E. Zarantonello, Academic Press, New York (1971), pp. 425500. MR 52:15143
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 K. C. Chang, Variational methods for nondifferentiable functionals and their applications to partial differential equations, J. Math. Anal. App. 80 (1981), pp. 102129.
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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:
http://dx.doi.org/10.1090/S0002993999049060
PII:
S 00029939(99)049060
Keywords:
Compact operator,
measurable multifunction,
lsc and usc multifunction,
multivalued Nemitsky operator,
$h$continuous multifunction,
LeraySchauder 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
