Abstract and Applied Analysis
Volume 4 (1999), Issue 3, Pages 153-168

Nonlocal boundary value problem for second order abstract elliptic differential equation

Mohamed Denche

Institut de Mathematiques, Université Mentouri Constantine, Constantine 25000, Algeria

Received 8 July 1999

Copyright © 1999 Mohamed Denche. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We establish conditions that guarantee Fredholm solvability in the Banach space Lp of nonlocal boundary value problems for elliptic abstract differential equations of the second order in an interval. Moreover, in the space L2 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.