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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
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.

References [Enhancements On Off] (What's this?)

  • [1] 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
  • [2] Rodney D. Driver, Existence and continuous dependence of solutions of a neutral functional-differential equation, Arch. Rational Mech. Anal. 19 (1965), 149–166. MR 0179406
  • [3] 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 0262633

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Keywords: Neutral-differential equations, functional equations, continuous dependence, existence theory
Article copyright: © Copyright 1971 American Mathematical Society