scholarly journals On zeros of the characteristic determinant of the spectral problem for a third-order differential operator on a segment with nonlocal boundary conditions

2013 ◽  
Vol 2013 (1) ◽  
Author(s):  
Nurlan S Imanbaev ◽  
Baltabek E Kanguzhin ◽  
Burkhan T Kalimbetov
Keyword(s):  
Differential Operator ◽  
Boundary Conditions ◽  
Spectral Problem ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Order Differential Operator ◽  
Third Order ◽  
Characteristic Determinant

ON THE SOLVABILITY OF A MIXED PROBLEM WITH DEGREE LAPLACE OPERATORS WITH NONLOCAL BOUNDARY CONDITIONS

2020 ◽  
pp. 85-104
Author(s):  
Shakirbai G. Kasimov ◽  
◽  
Mahkambek M. Babaev ◽  
◽  
Keyword(s):  
Boundary Conditions ◽  
Spectral Problem ◽  
Nonlocal Boundary ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlocal Boundary Conditions ◽  
Laplace Operators ◽  
Initial Boundary Problem ◽  
Initial Boundary Value ◽  
Delayed Time

The paper studies a problem with initial functions and boundary conditions for partial differential partial equations of fractional order in partial derivatives with a delayed time argument, with degree Laplace operators with spatial variables and nonlocal boundary conditions in Sobolev classes. The solution of the initial boundary-value problem is constructed as the series’ sum in the eigenfunction system of the multidimensional spectral problem. The eigenvalues are found for the spectral problem and the corresponding system of eigenfunctions is constructed. It is shown that the system of eigenfunctions is complete and forms a Riesz basis in the Sobolev subspace. Based on the completeness of the eigenfunctions system the uniqueness theorem for solving the problem is proved. In the Sobolev subspaces the existence of a regular solution to the stated initial-boundary problem is proved.

scholarly journals NONLOCAL THIRD ORDER BOUNDARY VALUE PROBLEMS WITH SOLUTIONS THAT CHANGE SIGN

2014 ◽  
Vol 19 (2) ◽  
pp. 145-154
Author(s):  
Sergey Smirnov
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Shooting Method ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Oscillatory Behavior ◽  
Third Order ◽  
Scaling Method ◽  
Number Of Solutions

We investigate the existence and the number of solutions for a third order boundary value problem with nonlocal boundary conditions in connection with the oscillatory behavior of solutions. The combination of the shooting method and scaling method is used in the proofs of our main results. Examples are included to illustrate the results.

scholarly journals Positivity of a differential operator with nonlocal conditions

Filomat ◽  
2016 ◽  
Vol 30 (3) ◽  
pp. 885-904
Author(s):  
Allaberen Ashyralyev ◽  
Nese Nalbant
Keyword(s):  
Differential Operator ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Parabolic Equations ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Nonlocal Conditions ◽  
Nonlocal Boundary Conditions ◽  
Nonlocal Boundary Value Problems ◽  
Fractional Spaces

In the present paper, the positivity of the differential operator with nonlocal boundary conditions is established. The structure of fractional spaces is investigated. In applications, we will obtain new coercive inequalities for the solution of local and nonlocal boundary value problems for parabolic equations.

scholarly journals SOLVABILITY OF BOUNDARY VALUE PROBLEMS WITH TRANSMISSION CONDITIONS FOR DISCONTINUOUS ELLIPTIC DIFFERENTIAL OPERATOR EQUATIONS

2016 ◽  
Vol 12 (1) ◽  
pp. 5842-5857
Author(s):  
Mustafa Kandemir
Keyword(s):  
Differential Operator ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Discontinuous Coefficients ◽  
Transmission Conditions ◽  
Elliptic Differential Operator ◽  
Operator Equations

We consider nonlocal boundary value problems which includes discontinuous coefficients elliptic differential operator equations of the second order and nonlocal boundary conditions together with boundary-transmission conditions. We prove coerciveness and Fredholmness for these nonlocal boundary value problems.

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