On one two-point boundary value problem for the system of evolutional differential equations

Abstract

In this paper there are established effective criteria for the existence and uniqueness of the solution of one two-point boutndary value problem for the system of differential equations with delays dx(t)=f (t,x(T1 (t)),....,x (Tm(t))) ----- dt x(0) = (1 - u)x(l) + uc, x(0) =(t) for tˇ0, where for a natural number n, an integer m, u ţ[0, 1], and the interval I = [0, l]ţR, the function f: I x R n(1+m) »Rn is a vector-valued function satisfying the local Carathočodory conditions, Tj : I»R (j = l,....m) are measurable functions such that Tj(t)ˇt (j=l,...m) for almost all tţI, cţRn, is a continuous and bounded vector-valued function.