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