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Zbl 1115.34076
El-Sayed, Wagdy G.
Solvability of a neutral differential equation with deviated argument. (English)
[J] J. Math. Anal. Appl. 327, No. 1, 342-350 (2007). ISSN 0022-247X

The paper deals with a functional-differential equation of the form $$x'(t)=f(t,x(H(t)),x'(h(t)))\text{ for }t\in[0,\infty)\tag 1.$$ Using the measure of non-compactness together with Schauder's fixed point theorem, the author proves the existence of a solution $y(t)$ of (1) such that $$\lim_{t\to\infty}y(t)\exp(-h(t))=0,$$ where the function $h:[0,\infty)\to[0,\infty)$ is continuous, non-decreasing, $h(t)\leq t$ and $\lim_{t\to\infty}h(t)=\infty$, $\lim_{t\to\infty}(t-h(t))=\infty$.
[Jan Ohriska (Košice)]

MSC 2000:: *34K40 Neutral equations

Keywords: Neutral equations

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