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Oscillation of second order functional differential equations with damping. (English) Zbl 1105.34326
Summary: Using a class of new test functions $\Phi(t,s,r)$ defined in our recent work [J. Math. Anal. Appl. 291, 341--351 (2004; Zbl 1061.34027)], we establish some new oscillation criteria for the second-order functional-differential equation with damping $$x''(t)+p(t)x'(t)+ \int^b_a q(t,\xi)f\biggl(x\bigl[g_1(t,\xi)\bigr], \dots,x \bigl[g_m(t,\xi)\bigr] \biggr)d\sigma(\xi)=0.$$ Our results are different from most known ones and can be applied to many cases which are not covered by existing results.

MSC:
34K11Oscillation theory of functional-differential equations
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References:
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