Nonoscillation of higher order functional differential equations. (English) Zbl 0535.34052
The objective of this paper is to obtain sufficient conditions for all solutions of the forced higher order nonlinear functional differential equation \((a(t)x')^{(n-1)}+f(x(g(t)))=r(t)\) to be nonoscillatory. For this purpose, the asymptotic behavior of oscillatory solutions is discussed. The main results refer to nonlinearities of the type \(| f(x)| \leq A| x|^ p+B\).
Reviewer: M.Boudourides
MSC:
| 34K99 | Functional-differential equations (including equations with delayed, advanced or state-dependent argument) |
| 34C15 | Nonlinear oscillations and coupled oscillators for ordinary differential equations |
| 34K25 | Asymptotic theory of functional-differential equations |
Keywords:
oscillatory solutions; nonoscillatory solutions; asymptotic properties; forced higher order nonlinear functional differential equationReferences:
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