SOME TWO-POINT BOUNDARY VALUE PROBLEMS FOR SYSTEMS OF HIGHER ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS

In the paper we study the question of the solvability and unique solvability of systems of the higher order differential equations with the argument deviations u(i)((mi)) (t) = p(i)(t)u(i+1) (tau(i) (t)) + q(i) (t), (i = (1, n) over bar), for t is an element of I := [a, b], and u(i)((mi)) (t) = F-i(n)(t) q(0i) (t), (i = ((1, n) over bar), for t is an element of I, under the conjugate u(i)((j1-1)) (a) = a(ij1), u(i)((j2-1)) (b) = b(ij2), j1 = (1, k(i)) over bar, j2 = (1, m(i) - k(i)) over bar, i = 1, n, and the right-focal u(i)((j1-1)) (a) = a(ij1), u(i)((j2-1)) (b) = b(ij2), j(1) = (1, k(i)) over bar, j2 = (k(i) + 1, m(i)) over bar, i = (1, n) over bar, boundary conditions, where u(n +1) = u(1), n >= 2, m(i) >= 2, p(i) is an element of L-infinity (I; R), q(i), q(0i) is an element of L(I; tau(i): I -> I are the measurable functions, k(i) are the local Caratheodory's class operators, and ki is the integer part of the number m(i)/2. In the paper are obtained the efficient sufficient conditions that guarantee the unique solvability of the linear problems and take into the account explicitly the effect of argument deviations, and on the basis of these results are proved new conditions of the solvability and unique solvability for the nonlinear problems.