Abstract and Applied Analysis
Volume 4 (1999), Issue 3, Pages 153-168
Nonlocal boundary value problem for second order abstract elliptic differential equation
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 of nonlocal boundary value problems for elliptic abstract differential equations of the second order in an interval. Moreover, in the space 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.