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Oscillation of second-order nonlinear ODE with damping. (English) Zbl 1122.34027
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.

MSC:
34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
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References:
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