Nonlocal boundary value problem for second order abstract elliptic differential equation

Abstract

We establish conditions that guarantee Fredholm solvability in the Banach space $L_p$ of nonlocal boundary value problems for elliptic abstract differential equations of the second order in an interval. Moreover, in the space $L_2$ we prove in addition the coercive solvability, and the completeness of root functions (eigenfunctions and associated functions). The obtained results are then applied to the study of a nonlocal boundary value problem for Laplace equation in a cylindrical domain.