Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 4, Number 3 (1999), 153-168.
Nonlocal boundary value problem for second order abstract elliptic differential equation
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.
Abstr. Appl. Anal., Volume 4, Number 3 (1999), 153-168.
First available in Project Euclid: 9 April 2003
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Zentralblatt MATH identifier
Primary: 35J05: Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation [See also 31Axx, 31Bxx] 35P20
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