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Oscillation theorems for second order nonlinear functional differential equations with damping. (English) Zbl 1057.34083

The paper deals with the second-order nonlinear differential equation \[ (a(t)x'(t))' + p(t) x'(\sigma(t))+ q(t)f(x(g(t)))=0.\tag{1} \] The authors advert several well-known oscillation criteria for second-order differential equations of simpler form than equation (1) and establish some sufficient conditions for every solution \(x(t)\) of (1) to be oscillatory or \(x(t)\to 0\) as \(t\to\infty\). Note that there are some misprints in the paper and some considerations are loaded with some inaccuracies.

MSC:

34K11 Oscillation theory of functional-differential equations
34K40 Neutral functional-differential equations
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