On a boundary value problem

Abstract

The equation x"(t) = /(t, i(a(<)), for t € [a, b], where the functions a,/? deviated argument of type [a,b] —• [a,b] is considered. A sufficient condition for existence of the end b of the interval [a, 6], 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 ||r'(a)|| = v > 0, where the constants o, v and vectors A, B are given, is proved.