## Solvability of a neutral differential equation with deviated argument.(English)Zbl 1115.34076

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 $$\lim_{t\to\infty}h(t)=\infty$$, $$\lim_{t\to\infty}(t-h(t))=\infty$$.

### MSC:

 34K40 Neutral functional-differential equations

### Keywords:

Neutral equations
Full Text:

### References:

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