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Proceedings of the American Mathematical Society

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Existence and continuous dependence for a class of nonlinear neutral-differential equations


Author: L. J. Grimm
Journal: Proc. Amer. Math. Soc. 29 (1971), 467-473
MSC: Primary 34.75
DOI: https://doi.org/10.1090/S0002-9939-1971-0287117-1
MathSciNet review: 0287117
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Abstract: This paper presents existence, uniqueness, and continuous dependence theorems for solutions of initial-value problems for neutral-differential equations of the form

$\displaystyle x'(t) = f(t,x(t),x(g(t,x)),x'(h(t,x))),\quad x(0) = {x_0},$

where f, g, and h are continuous functions with $ g(0,{x_0}) = h(0,{x_0}) = 0$. The existence of a continuous solution of the functional equation $ z(t) = f(t,z(h(t)))$ is proved as a corollary.

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DOI: https://doi.org/10.1090/S0002-9939-1971-0287117-1
Keywords: Neutral-differential equations, functional equations, continuous dependence, existence theory
Article copyright: © Copyright 1971 American Mathematical Society