Existence and uniqueness of solutions for nonlocal boundary vector value problems of ordinary differential systems with higher order
In this paper, we give existence and uniqueness results for solutions of nonlocal boundary vector value problems of the form x((n)) (t) = f (t, x (t), x' (t), ..., x((n-1)) (t)), t is an element of [0, 1], x(0) = x' (0) = (...) = x((n-2)) (0) = 0, x((n-1)) (1) = integral(0)(1) [dg (s)] x((n-1)) (s), where n greater than or equal to 2, f : [0, 1] x (R-N1)(n) --> R-N1 is a Caratheodory function, g : [0, 1] --> R-N1 x R-N1 is a Lebesgue measurable N-1 x N-1-matrix function and it satisfies g(0) = 0, the integral is in sense of Riemann-Stieltjes. The existence of a solutions is proven by the coincidence degree theory. As an application, we also give one example to demonstrate our results. (C) 2004 Elsevier Ltd. All rights reserved.
existence uniqueness coincidence degree higher-order system nonlocal boundary value problems fredholm operator