Abstract and Applied Analysis

Nonlocal boundary value problem for second order abstract elliptic differential equation

Mohamed Denche

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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.

Article information

Source
Abstr. Appl. Anal., Volume 4, Number 3 (1999), 153-168.

Dates
First available in Project Euclid: 9 April 2003

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1049907201

Digital Object Identifier
doi:10.1155/S1085337599000135

Mathematical Reviews number (MathSciNet)
MR1811233

Zentralblatt MATH identifier
0987.35044

Subjects
Primary: 35J05: Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation [See also 31Axx, 31Bxx] 35P20
Secondary: 34G10

Citation

Denche, Mohamed. Nonlocal boundary value problem for second order abstract elliptic differential equation. Abstr. Appl. Anal. 4 (1999), no. 3, 153--168. doi:10.1155/S1085337599000135. https://projecteuclid.org/euclid.aaa/1049907201


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