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Existence of nonoscillatory solutions of higher-order neutral differential equations with positive and negative coefficients. (English) Zbl 1025.34065
The authors consider the following higher-order neutral functional-differential equations with positive and negative coefficients: $$ \frac{d^n}{dt^n}[x(t)+cx(t-\tau)]+(-1)^{n+1}[P(t)x(t-\sigma)-Q(t)x(t-\delta)]=0,\quad t\geq t_0, $$ where $n\geq 1$ is an integer, $c\in \bbfR, \tau, \sigma, \delta \in\bbfR^+$, and $P, Q\in C([t_0, \infty), \bbfR^+), \bbfR^+=[0, \infty)$. They obtain global results (with respect to $c$) which are some sufficient conditions for the existence of nonoscillatory solutions.

34K11Oscillation theory of functional-differential equations
34K40Neutral functional-differential equations
Full Text: DOI
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