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Some results concerning second and third order neutral delay differential equations with piecewise constant argument. (English) Zbl 0817.34041

The results of the paper deal with existence, stability and oscillation of solutions to second- and third-order neutral delay differential equations with piecewise constant argument of the form \[ {d^ 2\over dt^ 2} (x(t)+ px(t- 1))= - qx(2[(t+ 1)/2]))\text{ and }{d^ 3\over dt^ 3} (x(t)+ px(t- 1))= - qx(2[(t+ 1)/2])), \] where \(t\in [-1, \infty)\), and \(p\), \(q\) are real constants.

MSC:

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

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