Existence of solutions of nth order impulsive integro-differential equations in Banach spaces

Comparison results for initial value problems of second-order impulsive integro-differential inclusions

“…By applying the change of variables s = −  R 2 r (1/t n−1 )dt, followed by the change of variables t = (m − s)/m, with m = −  R 2 R 1 (1/t n−1 )dt, (19) can be brought into the form    u ′′ (t) ∈ ρ(t)G(u(t)), 0 ≤ t ≤ 1, r ̸ = R, u| t=t R = −au(t R ) + bu ′ (t R ), u(0) = 0, u ′ (0) = 0.…”