On a boundary value problem - Kalinowski, Józef (Annales Mathematicae Silesianae, 1993)
The equation x"(t) = f(t,x(α(t)), x'(β(t))) for t∈[a,b], where the functions α, β deviated argument of type [a,b] → [a,b] is considered. A sufficient condition for existence of the end b of the interval [a,b], such that there exists the solution x of the above equation on [a,b] fulfilling the boundary value conditions x(a) = A, x(b) = B and ‖x'(a)‖ = v > 0, where the constants a, v and vectors A, B are given, is proved.