Semi-nonoscillation intervals and sign-constancy of Green’s functions of two-point impulsive boundary-value problems
UDC 517.9 We consider the second order impulsive differential equation with delays  $$(Lx)(t)\equiv x''(t) + \sum\limits _{j = 1}^{p} a_j(t) x'(t-\tau_j(t)) + \sum\limits _{j = 1}^{p} b_j(t) x(t-\theta_j(t)) = f(t),  \quad t \in [0, \omega],&...
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| Datum: | 2021 |
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| Hauptverfasser: | , , , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2021
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/473 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | UDC 517.9
We consider the second order impulsive differential equation with delays 
$$(Lx)(t)\equiv x''(t) + \sum\limits _{j = 1}^{p} a_j(t) x'(t-\tau_j(t)) + \sum\limits _{j = 1}^{p} b_j(t) x(t-\theta_j(t)) = f(t),  \quad t \in [0, \omega], $$ $$x(t_k) = \gamma_k x(t_k-0), \quad x'(t_k) = \delta_k x'(t_k-0),\quad  k = 1, 2, \ldots , r,$$
where $\gamma_k > 0,$ $\delta_k >0$ for $k = 1, 2, \ldots , r.$ In this paper, we obtain the conditions of semi-nonoscillation for the corresponding homogeneous equation on the interval $[0, \omega].$  Using these results, we formulate theorems on sign-constancy of Green's functions for two-point impulsive boundary-value problems in terms of differential inequalities. 
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| DOI: | 10.37863/umzh.v73i7.473 |