The well-posedness of the Bitsadze-Samarskii type nonlocal boundary value problem in Hlder spaces with a weight is established. The coercivity inequalities for the solution of the nonlocal boundary value problem for elliptic equations are obtained. The stable second order of accuracy difference scheme for the approximate solution of the problem is presented. The well-posedness of this difference scheme in difference analogue of Hlder spaces is established. For applications, the almost coercivity and the coercivity estimates for solutions of difference schemes for elliptic equations are obtained. (C) 2012 Elsevier Inc. All rights reserved.