Semi-nonoscillation intervals and sign-constancy of Green’s functions of two-point impulsive boundary-value problems - Domoshnitsky, A.; Mizgireva, Iu.; Raichik, V. (Ukrains’kyi Matematychnyi Zhurnal, 2021)
UDC 517.9 We consider the second order impulsive differential equation with delays (Lx)(t)x’’(t) + _j = 1^p a_j(t) x’(t-τ_j(t)) + _j = 1^p b_j(t) x(t-θ_j(t)) = f(t), t [0, ω], x(t_k) = γ_k x(t_k-0), x’(t_k) = δ_k x’(t_k-0),k = 1, 2, … , r, where γ_k > 0, δ_k >0 for k = 1, 2, … , r. In this paper, we obtain the conditions of semi-nonoscillation for the corresponding homogeneous equation on the interval [0, ω]. 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.