Semi-nonoscillation intervals and sign-constancy of Green’s functions of two-point impulsive boundary-value problems
Анотація
UDC 517.9
Інтервали майже вiдсутностi осциляцiй та збереження знаку функцiй Грiна двоточкових iмпульсних крайових задач
Розглядається імпульсне диференціальне рівняння другого порядку із запізненням
$$(Lx)(t)\equiv x''(t) + \sum\limits _{j = 1}^{p} a_j(t) x'(t-\tau_j(t)) + \sum\limits _{j = 1}^{p} b_j(t) x(t-\theta_j(t)) = f(t), \quad t \in [0, \omega], $$ $$x(t_k) = \gamma_k x(t_k-0), \quad x'(t_k) = \delta_k x'(t_k-0),\quad k = 1, 2, \ldots , r,$$
де $\gamma_k > 0,$ $\delta_k >0$ для $k = 1, 2, \ldots , r.$ Знайдено умови майже відсутності коливань для відповідного однорідного рівняння на інтервалі $[0, \omega].$ За допомогою цих результатів сформульовано теореми про збереження знака функцій Гріна двоточкових імпульсних крайових задач у термінах диференціальних нерівностей.
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