Eigenvalues and Eigenfunctions of Differential Operators with Involution

We demonstrate that the presence of summands with involution in the argument in an ordinary differential equation can significantly affect the well-posedness of the Cauchy and other problems. Furthermore, we show that the above effects can influence the well-posedness of classical boundary value pro...

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Bibliographic Details
Published in:Siberian mathematical journal Vol. 65; no. 5; pp. 1139 - 1149
Main Authors: Kozhanov, A. I., Bzheumikhova, O. I.
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 01.09.2024
Springer Nature B.V
Subjects:
Boundary value problems
Cauchy problems
Eigenvalues
Eigenvectors
Equality
Mathematics
Mathematics and Statistics
Operators (mathematics)
Ordinary differential equations
Partial differential equations
Well posed problems
517.927.2:517.956
solvability
differential equations with involution
well-posedness
nonlocal problem
Cauchy problem
ISSN:0037-4466, 1573-9260
Online Access:Get full text
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Summary:We demonstrate that the presence of summands with involution in the argument in an ordinary differential equation can significantly affect the well-posedness of the Cauchy and other problems. Furthermore, we show that the above effects can influence the well-posedness of classical boundary value problems for partial differential equations, particularly in the case of parabolic and pseudoparabolic equations.
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ISSN:0037-4466
1573-9260
DOI:10.1134/S0037446624050136