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Interval criteria for oscillation of second-order differential equations with mixed nonlinearities. (English) Zbl 1141.34317
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:
 34C10 Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
Full Text:
References:
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