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Oscillation theorems of comparison type of delay differential equations with a nonlinear damping term. (English) Zbl 0815.34061
The author studies oscillatory behaviour of solutions of delay- differential equations of the form $$(*)$$ $$L_ nx(t) + f(t,x (t-g)$$, $$x'(t-h)) = 0$$, where $$n$$ is even, $$L_ 0 x(t) = x(t)$$, $$L_ k x(t) = {1 \over a_ k(t)} (L_{k-1} x(t))'$$, $$k = 1,2, \dots,n$$, $$a_ n = 1$$, $$a_ i : [t_ 0, \infty) \to (0, \infty)$$, $$i = 1,2, \dots,n - 1$$, $$f : [t_ 0, \infty) \times R^ 2 \to R$$ are continuous, $$g$$ and $$h$$ are positive constants and $$h\geq g$$. He obtains his results by comparing $$(*)$$ with some delay-differential equations of the same or lower order but without the damping term whose oscillatory behaviour is known.

##### 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
##### Keywords:
oscillatory behaviour; delay-differential equations
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##### References:
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