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Existence Theory for Nonlinear Fredholm and Volterra Integrodifferential Equations

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Book cover Existence Theory for Nonlinear Integral and Integrodifferential Equations

Part of the book series: Mathematics and Its Applications ((MAIA,volume 445))

Abstract

In this chapter, a Nonlinear Alternative of Leray-Schauder type will be used to establish an existence principle for the operator equation

$$ \left\{ {\begin{array}{*{20}c} {y'(t) = V{\rm{ y(t)}}} \\ {y(0) = y_{0'} } \\\end{array}} \right. $$
(2.1.1)

on both the compact interval [0, T], and the half-open interval [0, T]. Various cases of the operator V will be discussed. In particular we consider cases when V is composed of either Fredholm or Volterra integral operators, which when coupled with (2.1.1), provide us with existence principles for Fredholm and Volterra integrodifferential equations.

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References

  1. H. Brezis and F. E. Browder, Existence theorems for nonlinear integral equations of Hammerstein type, Bull. Amer. Math. Soc., 81 (1975), 73–78.

    Article  MathSciNet  MATH  Google Scholar 

  2. C. Corduneanu, Integral Equations and Applications, Cambridge Univ. Press, New York, 1991.

    Book  MATH  Google Scholar 

  3. G. Gripenberg, S. O. Londen and O. Staffans, Volterra Integral and Functional Equations, Encyclopedia of Mathematics and its Applications, 34, Cambridge Univ. Press, New York, 1990.

    Google Scholar 

  4. R. B. Guenther and J. W. Lee, Some existence results for nonlinear integral equations via topological transversality, J. Integral Eqn. Appl., 5 (1993), 195–209.

    Article  MathSciNet  MATH  Google Scholar 

  5. J. W. Lee and D. O’Regan, Existence principles for nonlinear integral equations on semi-infinite and half-open intervals, Advances in Nonlinear Dynamics (edited by S. Sivasundarem and A. A. Martynyuk), Gordon and Breach Science Publishers Ltd., Amsterdam, 1997, 355–364.

    Google Scholar 

  6. M. Meehan and D. O’Regan, Existence theory for nonlinear Volterra integrodifferential and integral equations, Nonlinear Analysis, 31(1998), 317–341.

    Article  MathSciNet  MATH  Google Scholar 

  7. J. A. Nohel and D. F. Shea, Frequency domain methods for Volterra equations, Advances in Math., 22 (1976), 278–304.

    Article  MathSciNet  MATH  Google Scholar 

  8. D. O’Regan, Existence results for nonlinear integral equations, J. Math. Anal. Appl., 192 (1995), 705–726.

    Article  MathSciNet  MATH  Google Scholar 

  9. D. O’Regan, Existence theory for nonlinear Volterra and Hammerstein integral equations, Dynamical Systems and Applications, (edited by R. P. Agarwal), World Scientific Series in Applicable Analysis, River Edge, New Jersey, Vol. 4, 1995, 601–615.

    Chapter  Google Scholar 

  10. B. G. Pachpatte, Applications of the Leray-Schauder alternative to some Volterra integral and integrodifferential equations, Indian J. Pure Appl. Math., 26 (1995), 1161–1168.

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, National University of Ireland, Galway, Ireland

    Donal O’Regan & Maria Meehan

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  1. Donal O’Regan
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  2. Maria Meehan
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© 1998 Springer Science+Business Media Dordrecht

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O’Regan, D., Meehan, M. (1998). Existence Theory for Nonlinear Fredholm and Volterra Integrodifferential Equations. In: Existence Theory for Nonlinear Integral and Integrodifferential Equations. Mathematics and Its Applications, vol 445. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4992-1_2

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  • DOI: https://doi.org/10.1007/978-94-011-4992-1_2

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6095-0

  • Online ISBN: 978-94-011-4992-1

  • eBook Packages: Springer Book Archive

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