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
Abstract:
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.References
- 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
Additional Information
- © Copyright 1971 American Mathematical Society
- 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