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.


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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