In the present paper the abstract nonlocal boundary value problem for the second order differential equation -v"(t)+Av(t) = f(t) (0 ≤ t ≤ T),v(0) = v(T) + Φ, ∫ from 0 to T of v(s)ds = ψ in an arbitrary Banach space E with the positive operator A is considered. The well-posedness of this problem in various Banach spaces is established. In applications, the coercive stability estimates in Holder norms for the solutions of the mixed type nonlocal boundary value problems for elliptic equations are obtained.
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