New oscillation criteria for second-order nonlinear neutral delay differential equations. (English) Zbl 1175.34087

Liu, Lihua; Bai, Yuzhen

J. Comput. Appl. Math. 231, No. 2, 657-663 (2009); erratum ibid. 233, No. 10, 2755 (2010).

Summary: Several new oscillation criteria for the second-order nonlinear neutral delay differential equation
\[ [r(t)|x(t) + p(t)x[\sigma (t)])^{\prime }|^{m-1}(x(t) + p(t)x[\sigma (t)])^{\prime }]^{\prime } + q(t)f(x[\tau (t)]) = 0,\quad t \geq t_0 \]
are established. These oscillation criteria extend and improve some known results. An interesting example illustrating the importance of our results is also provided.

MSC:

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

Keywords:

oscillation; nonoscillatory solution; second-order; nonlinear neutral delay differential equation; new operator

References:

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