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Existence of nonoscillatory solutions of first order nonlinear neutral equations. (English) Zbl 0723.34069
Consider the nonlinear neutral equation \[ (x(t)-\sum^{n}_{1}P_ i(t)x(h_ i(t)))'+\sum^{n}_{1}f_ i(t,x(g_ i(t)))=Q(t) \] with continuous coefficients and asymptotically unbounded argument deviations. There are obtained necessary and sufficient conditions for the existence of a nonoscillatory solution with \(\liminf_{t\to \infty}| x(t)| >0\) or of a bounded nonoscillatory solution with \(\liminf_{t\to \infty}| x(t)| >0\).

MSC:
34K40 Neutral functional-differential equations
34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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