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Oscillation theorems for damped functional differential equations. (English) Zbl 0758.34053
The equations \(x''(t)+p(t)x'(t-r)-H(t,x(g(t)))=0\), \(x''(t)-p(t)x'(t+r)- H(t,x(g(t)))=0\) are considered, with \(H(t,x)\text{sign} x\geq q(t)| x|^ \lambda\). Criteria for oscillation are established, which fail if \(r=0\), and reduce to known ones if \(p=0\); 13 illustrative examples show the relevance of the results.

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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