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Oscillation of second-order sublinear impulsive differential equations. (English) Zbl 1223.34049
Summary: Oscillation criteria obtained by Kusano and Onose (1973) and by Belohorec (1969) are extended to second-order sublinear impulsive differential equations of Emden-Fowler type: $$x''(t) + p(t)|x(\tau(t))|^{\alpha - 1}x(\tau(t)) = 0,\quad t\ne\theta_k;$$ $$\Delta x'(t)|_{t=\theta_k} + q_k|x(\tau(\theta_k))|^{\alpha-1}x(\tau(\theta_{k})) = 0;\quad \Delta x(t)|_{t=\theta_{k}} = 0,\ (0 < \alpha < 1)$$ by considering the cases $\tau(t) \leq t$ and $\tau(t) = t$, respectively. Examples are inserted to show how impulsive perturbations greatly affect the oscillation behavior of the solutions.

MSC:
34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
34A37Differential equations with impulses
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Full Text: DOI
References:
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