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Oscillation criteria for a forced mixed type Emden-Fowler equation with impulses. (English) Zbl 1193.34067

The authors study the oscillation of the following forced mixed type Emden-Fowler equation with impulses
\[ \begin{cases} (r(t)x'(t))'+p(t)x(t)+\displaystyle\sum_{i=1}^np_i(t)|x(t)|^{\alpha_i-1}x(t)=e(t), \;t\neq\tau_k,\\ x(\tau_k^{+})=a_kx(\tau_k), \;x'(\tau_k^{+})=b_kx'(\tau_k). \end{cases}\tag{*} \]
By employing the arithmetic-geometric mean inequality, the authors obtain some oscillation criteria of for (*). When the impulses are dropped, the results of this paper extend some known results.

MSC:

34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34A37 Ordinary differential equations with impulses
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References:

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