Two-point boundary value problems for differential-operator equations

Abstract

We study general two-point boundary value problems for a non-homogeneous differential-operator equation of the second order with an unbounded linear operator in a Banach space. The main classical solvability condition is given in terms of the property of the resolvent of the operator at the points, which are opposite to the eigenvalues of the corresponding ordinary differential operator. At the end of the paper, two particular types of boundary value conditions are treated: periodic and Dirichlet.