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Integral equations in reflexive Banach spaces and weak topologies
Author(s):
Donal
O'Regan
Journal:
Proc. Amer. Math. Soc.
124
(1996),
607-614.
MSC (1991):
Primary 45D05, 45G10, 45N05
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Abstract:
The Schauder Tychonoff theorem in a locally convex topological space is used to establish existence results for Volterra-Hammerstein and Hammerstein integral equations in a reflexive Banach space.
References:
- 1
- C. Corduneanu, Integral equations and stability of feedback systems, Academic Press, New York, 1973. MR 50:10710
- 2
- ------, Integral equations and applications, Cambridge Univ. Press, New York, 1991.MR 92h:45001
- 3
- ------, Perturbations of linear abstract Volterra equations, J. Integral Equations Appl. 2 (1990), 393--401.MR 92a:45005
- 4
- J. B. Conway, A course in functional analysis, Springer-Verlag, Berlin, 1990.MR 91e:46001
- 5
- E. J. Cramer, V. Lakshmikantham, and A. R. Mitchell, On the existence of weak solutions of differential equations in nonreflexive Banach spaces, Nonlinear Anal. 2, (1978), 169--177.MR 81d:34051
- 6
- C. De Vito, Functional analysis, Academic Press, New York, 1978.MR 80d:46001
- 7
- N. Dunford and J. T. Schwartz, Linear operators, Interscience, Wiley, New York, 1958.MR 22:8302
- 8
- K. Floret, Weakly compact sets, Lecture Notes in Math., vol. 801, Springer-Verlag, Berlin, 1980.MR 82b:46001
- 9
- G. Gripenberg, S. O. Londen, and O. Staffans, Volterra integral and functional equations, Cambridge Univ. Press, New York, 1990.MR 91c:45003
- 10
- R. B. Guenther and J. W. Lee, Some existence results for nonlinear integral equations via topological transversality, J. Integral Equations Appl. 5 (1993), 195--209.MR 94f:45009
- 11
- E. Hille, Methods in classical and functional analysis, Addison-Wesley, Reading, MA, 1972.MR 57:3802
- 12
- E. Hille and R. S. Phillips, Functional analysis and semigroups, Amer. Math. Soc. Colloq. Publ., vol. 31, Amer. Math. Soc., Providence, RI, 1957.MR 19:664d
- 13
- V. Lakshmikantham and S. Leela, Nonlinear differential equations in abstract spaces, Pergamon Press, Oxford, 1981.MR 82i:34072
- 14
- A. Szep, Existence theorems for weak solutions of ordinary differential equations in reflexive Banach spaces, Studia Sci. Math. Hungar. 6, (1971), 197--203.
- 15
- K. Yosida, Functional analysis, Springer-Verlag, Berlin, 1971.
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Additional Information:
Donal
O'Regan
Affiliation:
Department of Mathematics, University College Galway, Galway, Ireland
Email:
Donal.ORegan@ucg.ie
DOI:
10.1090/S0002-9939-96-03154-1
PII:
S 0002-9939(96)03154-1
Received by editor(s):
April 22, 1994
Received by editor(s) in revised form:
September 21, 1994
Communicated by:
Palle E. T. Jorgensen
Copyright of article:
Copyright
1996,
American Mathematical Society
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