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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:

34K11 Oscillation theory of functional-differential equations

Citations:

Zbl 1061.34027
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References:

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