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Zbl 1195.34098
Hasanbulli, Mustafa; Rogovchenko, Yuri V.
Oscillation criteria for second order nonlinear neutral differential equations.
(English)
[J] Appl. Math. Comput. 215, No. 12, 4392-4399 (2010). ISSN 0096-3003

The paper deals with the oscillatory behavior of second order nonlinear neutral delay differential equations of the form $$(r(t)(x(t)+p(t)x(t-\tau))')'+q(t)f(x(t),x(\sigma(t)))=0,\tag1$$ where $t\geq t_0>0$, $\tau\geq 0$ is a constant, and moreover $r,\sigma\in C^1([t_0,\infty),(0,\infty))$, $p,q\in C([t_0,\infty),\Bbb R)$, and $f\in C(\Bbb R^2,\Bbb R)$. The purpose of the paper is to improve oscillation results obtained for equation (1) by {\it W. Shi} and {\it P. Wang} [Appl. Math. Comput. 146, No.~1, 211--226 (2003; Zbl 1037.34059)] using a generalized Riccati transformation and developing ideas exploited by {\it Yu. V. Rogovchenko} and {\it F. Tuncay} [Nonlinear Anal., Theory Methods Appl. 69, No.~1 (A), 208--221 (2008; Zbl 1147.34026)]. Two examples are provided to illustrate the relevance of obtained results.
[Jan Ohriska (Košice)]
MSC 2000:
*34K11 Oscillation theory of functional-differential equations
34K40 Neutral equations

Keywords: nonlinear neutral differential equations; oscillatory solutions; second order; asymptotic behavior

Citations: Zbl 1037.34059; Zbl 1147.34026

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