Nonlocal boundary value problem for second order abstract elliptic differential equation. (1999) - Denche, Mohamed
Abstract : We establish conditions that guarantee Fredholm solvability in the Banach spaceL p of nonlocal boundary value problems for elliptic abstract differential equations of the second order in an interval. Moreover, in the spaceL 2 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.