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
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.
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