On the uniqueness of the solution of an inverse problem of spectral analysis for a singular second-order ordinary differential operator

2001 ◽  
Vol 56 (3) ◽  
pp. 578-579
Author(s):  
V V Dubrovskii ◽  
A N Tipko
Keyword(s):  
Inverse Problem ◽  
Spectral Analysis ◽  
Differential Operator ◽  
Second Order ◽  
Ordinary Differential Operator ◽  
Uniqueness Of The Solution

scholarly journals Riesz Inequality for the System of Root Functions of Second Order Ordinary Differential Operator

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Differential Operator ◽  
Sufficient Conditions ◽  
Second Order ◽  
Ordinary Differential Operator ◽  
Root Functions ◽  
Riesz Property ◽  
System Of Root Functions ◽  
The Given ◽  
Riesz Inequality

An ordinary differential operator of second order with coefficients is considered. The Riesz property of the system of root functions of the given operator is studied. The criterion of Bessel property in 2 L , of root functions system is established and use it to obtain sufficient conditions for the Riesz property of a system of normalized root functions of this operator in p L .

scholarly journals Basis Properties of Eigenfunctions of Second-Order Differential Operators with Involution

2012 ◽  
Vol 2012 ◽  
pp. 1-6 ◽  
Author(s):  
Asylzat Kopzhassarova ◽  
Abdizhakhan Sarsenbi
Keyword(s):  
Differential Operator ◽  
Differential Operators ◽  
Second Order ◽  
Ordinary Differential Operator ◽  
Spectral Problems ◽  
Associated Functions ◽  
Eigenfunctions And Associated Functions

We study the basis properties of systems of eigenfunctions and associated functions for one kind of generalized spectral problems for a second-order ordinary differential operator.

scholarly journals The Stabilization of the Solution of an inverse Problem for the Pseudoparabolic Equation

2021 ◽  
Vol 2092 (1) ◽  
pp. 012009
Author(s):  
A. Sh. Lyubanova ◽  
A. V. Velisevich
Keyword(s):  
Inverse Problem ◽  
Asymptotic Behavior ◽  
Differential Operator ◽  
Strong Solution ◽  
Second Order ◽  
Unknown Coefficient ◽  
Pseudoparabolic Equation

Abstract The asymptotic behavior of the strong solution to the inverse problem on recovering an unknown coefficient k(t) in a pseudoparabolic equation (u + ηMu) t + Mu + k(t)u = f is investigated. The differential operator M of the second order with respect spacial variables is supposed to be elliptic and selfajoint. It is proved that the solution of the inverse problem stabilizes to the solution of the appropriate stationary inverse problem as t → + ∞.

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