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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
##### Keywords:
functional differential equations; oscillation; examples