Uniqueness of Solutions of Some Nonlocal Boundary-Value Problems for Operator-Differential Equations on a Finite Segment

Abstract

For the equation L ₀ x(t) + L ₁ x ⁽¹⁾(t) + ... + L _n x ⁽ⁿ⁾(t) = 0, where L _k, k = 0, 1, ... , n, are operators acting in a Banach space, we formulate conditions under which a solution x(t) that satisfies some nonlocal homogeneous boundary conditions is equal to zero.