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Zbl 1222.34078
Dorociaková, Božena; Najmanová, Anna; Olach, Rudolf
Existence of nonoscillatory solutions of first-order neutral differential equations.
(English)
[J] Abstr. Appl. Anal. 2011, Article ID 346745, 9 p. (2011). ISSN 1085-3375; ISSN 1687-0409/e

Summary: This paper is concerned with the existence of a positive solution which is bounded below and above by positive functions of neutral differential equations of the form $$\tfrac{d}{dt}[x(t)-a(t)x(t-\tau)]=p(t)f(x(t-\sigma)),\quad t\ge t_0,\tag1$$ where $\tau>0$, $\sigma\ge 0$, $a\in C([t_0,\infty))$, $p\in C(\Bbb R,(0,\infty))$, $d\in C(\Bbb R,\Bbb R)$, $f\in C(\Bbb R,\Bbb R)$, $f$ is a nondecreasing function, and $xf(x)>0$, $x\ne 0$.
MSC 2000:
*34K11 Oscillation theory of functional-differential equations
34K40 Neutral equations

Keywords: positive solutions

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