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Oscillation theorems for nth-order delay differential equations. (English) Zbl 0546.34055

The paper discusses the oscillation behavior of the functional differential equations \(x^{(n)}+p(t)f(x(g(t)))=0\) (n even) and \[ x^{(n)}+p(t)| x^{(n-1)}|^{\beta}x^{(n- 1)}+q(t)f(x(g(t)))=0\quad (n\quad even,\quad\beta \geq 0) \] through the use of weighted integrals. The paper generalizes earlier standard results for the oscillations of delay differential equations which yield substantially improved results in the above situation.
Reviewer: B.A.Stephan

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
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