Existence and stability of a class of nonlinear Volterra integral equations

Author:
Stanley I. Grossman

Journal:
Trans. Amer. Math. Soc. **150** (1970), 541-556

MSC:
Primary 45.30

DOI:
https://doi.org/10.1090/S0002-9947-1970-0265886-8

MathSciNet review:
0265886

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Abstract: In this paper we study the problem of existence and uniqueness to solutions of the nonlinear Volterra integral equation , where the are continuous linear operators mapping a Fréchet space into itself and the are nonlinear operators in that space. Solutions are sought which lie in a Banach subspace of having a stronger topology. The equations are studied first when the are of the form where is ``small", and then when the are slope restricted. This generalizes certain results in recent papers by Miller, Nohel, Wong, Sandberg, and Beneš.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1970-0265886-8

Keywords:
Volterra integral equation,
nonlinear integral equation,
applications of contraction map,
integral equation resolvent,
convolution equations,
Fréchet space,
completely monic function,
Laplace-Stieltjes transform,
multiple resolvent,
slope restrictions,
nonlinear network

Article copyright:
© Copyright 1970
American Mathematical Society