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Forced oscillation of super-half-linear impulsive differential equations. (English) Zbl 1141.34024

The aim of this work is to establish new oscillation criteria for forced super-half-linear equations of the form
\[ \begin{alignedat}{2} 2 (m(t)\varphi_\alpha(y'))'&+ q(t)\varphi_\beta(y)= f(t),&\quad t&\neq \theta_i,\\ \Delta(m(t)\varphi_\alpha(y'))&+ q_i\varphi_\beta(y)= f_i,&\quad t&= \theta_i,\;i\in\mathbb{N}, \end{alignedat} \]
where \(\beta\geq \alpha\), \(m\), \(q\), \(f\in\text{PLC}(J)\), \(m(t)> 0\), \(t\in J\), \(\{q_i\}\) and \(\{f_i\}\) are sequences of real numbers. A Picone type formula in comparison with oscillatory unforced half-linear equations is used. In particular, the forced superlinear impulsive differential equation is considered.

MSC:

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

Keywords:

impulse
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References:

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