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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Admissibility and nonlinear Volterra integral equations

Author: R. K. Miller
Journal: Proc. Amer. Math. Soc. 25 (1970), 65-71
MSC: Primary 45.13
MathSciNet review: 0257674
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Abstract: Nonlinear perturbations of linear Volterra integral equations are studied in an abstract setting which contains and generalizes some earlier results on the same problem. The perturbed problem is first written as a variation of constants equation on a Fréchet space. It is then shown that standard fixed point theorems may be applied if the linear equation is admissible w.r.t. a Banach subspace of the Fréchet space. This theory is applied to an example where ${L^2}$-stability is proved.

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Keywords: Nonlinear Volterra integral equations, perturbations theory, stability theory, admissibility
Article copyright: © Copyright 1970 American Mathematical Society