Journal of Integral Equations and Applications

A Note on Solutions in $L^1[0,1]$ to Hammerstein Integral Equations

Donal O'Regan

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J. Integral Equations Applications, Volume 9, Number 2 (1997), 165-178.

First available in Project Euclid: 5 June 2007

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Hammerstein existence integral equations


O'Regan, Donal. A Note on Solutions in $L^1[0,1]$ to Hammerstein Integral Equations. J. Integral Equations Applications 9 (1997), no. 2, 165--178. doi:10.1216/jiea/1181076002.

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  • R.A. Adams, Sobolev spaces, Academic Press, New York, 1975.
  • J. Banas, Integrable solutions of Hammerstein and Urysohn integral equations, J. Australian Math. Soc. 46 (1989) 61-68.
  • J. Banas and W.G. El-Sayed, Measures of noncompactness and solvability of an integral equation in the class of functions of locally bounded variation, J. Math. Anal. Appl. 167 (1992), 133-151.
  • H. Brezis, Analyse fonctionnelle, theorie et applications, Masson, Paris, 1993.
  • C. Corduneanu, Integral equations and applications, Cambridge Univ. Press, New York, 1990.
  • J. Dugundji and A. Granas, Fixed point theory, Monografie Mathematyczne, PWN, Warsaw, 1982.
  • N. Dunford and J.T. Schwartz, Linear operators, Interscience/Wiley, New York, 1958.
  • G. Emmanuele, Integrable solutions of Hammerstein integral equations, Appl. Anal. 50 (1993), 277-284.
  • --------, Integrable solutions of a functional-integral equation, J. Integral Equations Appl. 4 (1992), 89-94.
  • G. Gripenberg, S.O. Londen and O. Staffans, Volterra integral and functional equations, Cambridge Univ. Press, New York, 1990.
  • L.V. Kantorovich and G.P. Akilov, Functional analysis, Pergamon, Oxford, 1982.
  • M.A. Krasnoselskii, Topological methods in the theory of nonlinear integral equations, Macmillan Co., New York, 1964.
  • C. Swartz, Measure, integration and function spaces, World Scientific, Singapore, 1994.
  • A. Torchinsky, Real variables, Addison Wesley, Redwood City, 1988.