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Oscillation criteria for nonlinear differential systems with general deviating of mixed type. (English) Zbl 0733.34072

The following system with deviating arguments of mixed type \[ (1)\quad \dot y_ i=p_ i(t)y_{i+1}(h_{i+1}(t)),\quad i=1,...,n-1,\quad \dot y_ n=\pm \sum^{N}_{m=1}a_ m(t)f_ m(y_ 1(g_ m(t)) \] is considered. Functions at the right-hand side are supposed to be continuous on \([0,\infty)\). A solution of (1) is said to be the proper one if it is of class \(C^ 1([T_ y,\infty))\) and sup\(\{\sum^{n}_{i=1}| y_ i(t)|\), \(t\geq T\}>0\) for any \(T\geq T_ y\). The author studies the oscillatory properties of proper solutions of the system (1).

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
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
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