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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Existence and continuous dependence for a class of nonlinear neutral-differential equations
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by L. J. Grimm PDF
Proc. Amer. Math. Soc. 29 (1971), 467-473 Request permission


This paper presents existence, uniqueness, and continuous dependence theorems for solutions of initial-value problems for neutral-differential equations of the form \[ x’(t) = f(t,x(t),x(g(t,x)),x’(h(t,x))),\quad x(0) = {x_0},\] 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.
  • Rodney D. Driver, A functional-differential system of neutral type arising in a two-body problem of classical electrodynamics, Internat. Sympos. Nonlinear Differential Equations and Nonlinear Mechanics, Academic Press, New York, 1963, pp. 474–484. MR 0146486
  • Rodney D. Driver, Existence and continuous dependence of solutions of a neutral functional-differential equation, Arch. Rational Mech. Anal. 19 (1965), 149–166. MR 179406, DOI 10.1007/BF00282279
  • J. K. Hale and M. A. Cruz, Existence, uniqueness and continuous dependence for hereditary systems, Ann. Mat. Pura Appl. (4) 85 (1970), 63–81. MR 262633, DOI 10.1007/BF02413530
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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 29 (1971), 467-473
  • MSC: Primary 34.75
  • DOI:
  • MathSciNet review: 0287117