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Abstract and Applied Analysis

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Abstract and Applied Analysis / 1999 / Article

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Volume 4 |Article ID 207419 | https://doi.org/10.1155/S1085337599000135

Mohamed Denche, "Nonlocal boundary value problem for second order abstract elliptic differential equation", Abstract and Applied Analysis, vol. 4, Article ID 207419, 16 pages, 1999. https://doi.org/10.1155/S1085337599000135

Nonlocal boundary value problem for second order abstract elliptic differential equation

Mohamed Denche1

1Institut de Mathematiques, Université Mentouri Constantine, Algeria

Received08 Jul 1999

Abstract

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.

Copyright © 1999 Hindawi Publishing Corporation. 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.

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