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Zbl 1141.34317
Sun, Yuan Gong; Meng, Fan Wei
Interval criteria for oscillation of second-order differential equations with mixed nonlinearities. (English)
[J] Appl. Math. Comput. 198, No. 1, 375-381 (2008). ISSN 0096-3003

Summary: We establish interval criteria for oscillation of the second order forced ordinary differential equations with mixed nonlinearities: $$(p(t)x')'+q(t)x+\sum^n_{i=1}q_i(t)|x|^{\alpha_i}\text{sgn\,}x=e(t),$$ where $p(t$), $q(t)$, $q_i(t)$, $e(t)$ are continuous functions defined on $[0,\infty)$, $p(t)$ is positive and differentiable, $\alpha_1 >\cdots >a_m > 1 > a_{m+1} >\cdots > a_n > 0$ $(n > m \ge 1)$. No restriction is imposed on the potentials $q(t)$, $q_i(t)$ and $e(t)$ to be nonnegative.

MSC 2000:: *34C10 Qualitative theory of oscillations of ODE: Zeros, etc.

Keywords: interval criterion; second order; forced differential equation

Cited in: Zbl 1169.34332 Zbl 1155.35362

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