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On monotone and oscillating solutions of \(n\)-th order differential equations with retarded argument. (Russian) Zbl 0743.34075

The author studies the following \(n\)-th order nonlinear differential equation with delay: (1) \(u^{(n)}(t)+f(t,u(\tau_ 1(t)),\ldots,u(\tau_ m(t))=0\), establishing some sufficient conditions under which the equation (1) has no Kneser type solutions. Also some oscillation conditions for (1) are given.

MSC:

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
34C11 Growth and boundedness of solutions to ordinary differential equations
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