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Zbl 1122.34027
Zhao, Xueqin; Meng, Fanwei
Oscillation of second-order nonlinear ODE with damping.
(English)
[J] Appl. Math. Comput. 182, No. 2, 1861-1871 (2006). ISSN 0096-3003

The authors consider the differential equation $$(r(t)k_1(x(t),x'(t)))'+p(t)k_2(x(t),x'(t))x'(t)+ q(t)f(x(t))=0,\qquad t\geq t_0,\tag{1}$$ where $t_0$ is a fixed real number, $r\in C([t_0,+\infty);(0,+\infty))$, $p,q\in C([t_0,+\infty);\Bbb R)$, $f\in C(\Bbb R;\Bbb R)$, and $k_1,k_2\in C(\Bbb R^2;\Bbb R)$. Conditions are established guaranteeing that $(1)$ is oscillatory.
[Aleksandr Lomtatidze (Brno)]
MSC 2000:
*34C10 Qualitative theory of oscillations of ODE: Zeros, etc.

Keywords: Oscillation; nonlinear damping term; Riccati technique

Cited in: Zbl 1156.34024 Zbl 1193.34066

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