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Proceedings of the American Mathematical Society

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Integral equations in reflexive Banach spaces and weak topologies

Author: Donal O'Regan
Journal: Proc. Amer. Math. Soc. 124 (1996), 607-614
MSC (1991): Primary 45D05, 45G10, 45N05
MathSciNet review: 1301043
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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.

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  • 1 Constantin Corduneanu, Integral equations and stability of feedback systems, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1973. Mathematics in Science and Engineering, Vol. 104. MR 0358245
  • 2 C. Corduneanu, Integral equations and applications, Cambridge University Press, Cambridge, 1991. MR 1109491
  • 3 C. Corduneanu, Perturbation of linear abstract Volterra equations, J. Integral Equations Appl. 2 (1990), no. 3, 393–401. MR 1094476,
  • 4 John B. Conway, A course in functional analysis, 2nd ed., Graduate Texts in Mathematics, vol. 96, Springer-Verlag, New York, 1990. MR 1070713
  • 5 Evin Cramer, V. Lakshmikantham, and A. R. Mitchell, On the existence of weak solutions of differential equations in nonreflexive Banach spaces, Nonlinear Anal. 2 (1978), no. 2, 169–177. MR 512280,
  • 6 Carl L. DeVito, Functional analysis, Pure and Applied Mathematics, vol. 81, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. MR 506238
  • 7 Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, With the assistance of W. G. Bade and R. G. Bartle. Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers, Ltd., London, 1958. MR 0117523
  • 8 Klaus Floret, Weakly compact sets, Lecture Notes in Mathematics, vol. 801, Springer, Berlin, 1980. Lectures held at S.U.N.Y., Buffalo, in Spring 1978. MR 576235
  • 9 G. Gripenberg, S.-O. Londen, and O. Staffans, Volterra integral and functional equations, Encyclopedia of Mathematics and its Applications, vol. 34, Cambridge University Press, Cambridge, 1990. MR 1050319
  • 10 R. B. Guenther and J. W. Lee, Some existence results for nonlinear integral equations via topological transversality, J. Integral Equations Appl. 5 (1993), no. 2, 195–209. MR 1229437,
  • 11 Einar Hille, Methods in classical and functional analysis, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1972. Addison-Wesley Series in Mathematics. MR 0463863
  • 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, International Series in Nonlinear Mathematics: Theory, Methods and Applications, vol. 2, Pergamon Press, Oxford-New York, 1981. MR 616449
  • 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

Received by editor(s): April 22, 1994
Received by editor(s) in revised form: September 21, 1994
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society