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Oscillation of functional differential equations with general deviating arguments. (English) Zbl 0599.34091

The author proves a number of criteria for the following differential equations \(L_ nx(t)+\sum^{N}_{i=1}q_ i(t)x(g_ i(t))=0\) and \(L_ nx(t)+\sum^{N}_{i=1}q_ i(t)f_ i(x(g_ i(t)))=0\) to be oscillatory or almost oscillatory (in a sense that is made precise in the introduction). Here \(L_ n\) is a disconjugate differential operator defined by the recursion \(L_ 0x=x\), \(L_ ix=\frac{1}{p_ i}\frac{d}{dt}(L_{i-1}x),\) \(1\leq i\leq n\); \(p_ n=1\), where \(p_ 1,...,p_{n-1}\) are positive valued functions. The results presented extend and/or unify some of the previous results obtained in the oscillation theory of differential delayed equations. An interesting point here is that the deviating arguments \(g_ i\) are of general type.
Reviewer: M.M.Konstantinov

MSC:

34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
34A34 Nonlinear ordinary differential equations and systems
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34A30 Linear ordinary differential equations and systems
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