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Oscillation of second-order neutral functional differential equations with mixed nonlinearities. (English) Zbl 1210.34094

Summary: We study the following second-order neutral functional differential equation with mixed nonlinearities
\[ (r(t)|(u(t)+p(t)u(t-\sigma))'|^{\alpha-1}(u(t)+p(t)u(t-\sigma))')'+q_0(t)|u(\tau_0))|^{\alpha-1}u(\tau_0(t)) \]
\[ +q_1(t)|u(\tau_1(t))|^{\beta-1}u(\tau_1(t))+q_2(t)|u(\tau_2(t))|^{\gamma-1}u(\tau_2(t))=0, \]
where \(\gamma>\alpha>\beta>0\), \(\int^\infty_{t_0}(1/r^{1/\alpha}(t))\,dt<\infty\). Oscillation results for the equation are established which improve known results.

MSC:

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

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