scholarly journals Transmutation operators and a new representation for solutions of perturbed Bessel equations

2021 ◽  
Author(s):  
Vladislav V. Kravchenko ◽  
Sergii M. Torba
Keyword(s):  
Transmutation Operators

scholarly journals Nonlocal multipoint problem for a differential equation of $2n$-th order with operator coefficients

2021 ◽  
Vol 13 (2) ◽  
pp. 501-514
Author(s):  
Ya.O. Baranetskij ◽  
I.I. Demkiv ◽  
A.V. Solomko ◽  
O.M. Sus'
Keyword(s):  
Differential Equation ◽  
Existence And Uniqueness ◽  
Spectral Properties ◽  
Multipoint Problem ◽  
Root Functions ◽  
Multiple Eigenvalues ◽  
Finite Set ◽  
Uniqueness Of The Solution ◽  
Differential Operator Equation ◽  
Transmutation Operators

In the article, the spectral properties of a multipoint problem for a differential operator equation of order $2n$ are studied. The operator of the problem has an infinite number of multiple eigenvalues. Each multiple eigenvalue corresponds to a finite set of root functions. A commutative group of transmutation operators is constructed. Each element of the group corresponds to the isospectral perturbation of the problem operator with antiperiodic conditions. The conditions for the existence and uniqueness of the solution are established for the selected family of multipoint problems, and this solution is constructed too.

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