The accuracy of the solution of a difference boundary value problem for a fourth-order elliptic operator with mixed boundary conditions

1986 ◽  
Vol 26 (6) ◽  
pp. 139-147 ◽  
Author(s):  
I.P. Gavrilyuk ◽  
V.G. Prikazchikov ◽  
A.N. Khimich
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Elliptic Operator ◽  
Fourth Order ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Mixed Boundary Conditions ◽  
Order Elliptic Operator

scholarly journals The nonlocal boundary value problem with perturbations of mixed boundary conditions for an elliptic equation with constant coefficients. II

2020 ◽  
Vol 12 (1) ◽  
pp. 173-188
Author(s):  
Ya.O. Baranetskij ◽  
P.I. Kalenyuk ◽  
M.I. Kopach ◽  
A.V. Solomko
Keyword(s):  
Elliptic Equation ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Nonlocal Conditions ◽  
Mixed Boundary Conditions ◽  
Multipoint Problem ◽  
Uniqueness Of The Solution

In this paper we continue to investigate the properties of the problem with nonlocal conditions, which are multipoint perturbations of mixed boundary conditions, started in the first part. In particular, we construct a generalized transform operator, which maps the solutions of the self-adjoint boundary-value problem with mixed boundary conditions to the solutions of the investigated multipoint problem. The system of root functions $V(L)$ of operator $L$ for multipoint problem is constructed. The conditions under which the system $V(L)$ is complete and minimal, and the conditions under which it is the Riesz basis are determined. In the case of an elliptic equation the conditions of existence and uniqueness of the solution for the problem are established.

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