A problem with two nonlocal boundary conditions for a mixed-type equation

1999 ◽  
Vol 40 (6) ◽  
pp. 1064-1078 ◽  
Author(s):  
M. E. Lerner ◽  
O. A. Repin
Keyword(s):  
Boundary Conditions ◽  
Mixed Type ◽  
Nonlocal Boundary ◽  
Type Equation ◽  
Nonlocal Boundary Conditions ◽  
Mixed Type Equation

A nonlocal boundary-value problem for a fourth-order mixed-type equation

2020 ◽  
Vol 17 (1) ◽  
pp. 30-40
Author(s):  
Kudratillo Fayazov ◽  
Ikrombek Khajiev
Keyword(s):  
Fourth Order ◽  
Mixed Type ◽  
Nonlocal Boundary ◽  
Type Equation ◽  
Small Denominators ◽  
Mixed Type Equation ◽  
The Stability ◽  
Criterion Of Uniqueness ◽  
Uniqueness Of A Solution ◽  
Stability Of The Solution

The criterion of uniqueness of a solution of the problem with periodicity and nonlocal and boundary conditions is established by the spectral analysis for a fourth-order mixed-type equation in a rectangular region. When constructing a solution in the form of the sum of a series, we use the completeness in the space L_2, the system of eigenfunctions of the corresponding problem orthogonally conjugate. When proving the convergence of a series, the problem of small denominators arises. Under some conditions imposed on the parameters of the data of the problem and given functions, the stability of the solution is proved.

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