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On the existence of solutions of neutral functional differential equations of Carathéodory type. (Chinese. English summary) Zbl 0628.34065
Consider a general type of neutral functional differential equations (1) \((d/dt)D(t,x_ t,\lambda)=f(t,x_ t,\lambda).\) The existence theorems of solutions to retarded-type equations, neutral equations with continuous function f and retarded g-type equations with discontinuous function f were established by J. K. Hale [J. Differ. Equations 9, 168-181 (1971; Zbl 0213.36901)], M. A. Cruz and J. K. Hale [J. Math. Anal. Appl. 34, 267-288 (1971; Zbl 0218.34062)] and J. K. Hale [Theory of functional differential equations (1977; Zbl 0352.34001)], respectively. In this paper the author generalizes these theorems for (1) under the assumption that \(f(t,x_ t,\lambda)\) are discontinuous but satisfy the Carathéodory condition for \((t,\phi)\in \Omega\) uniformly with respect to \(\lambda\in \Lambda\).
Reviewer: Jinghuang Tian
34K05 General theory of functional-differential equations