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Sibirsk. Mat. Zh., 2024 Volume 65, Number 5, Pages 953–964 (Mi smj7902)

Eigenvalues and eigenfunctions of differential operators with involution

A. I. Kozhanova, O. I. Bzheumikhovab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Kabardino-Balkar State University, Nal'chik

Abstract: 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.

Keywords: differential equations with involution, Cauchy problem, well-posedness, nonlocal problem, solvability.

UDC: 517.927.2+517.956

MSC: 34B09, 34B10, 35K20

Received: 12.08.2024
Revised: 12.08.2024
Accepted: 20.08.2024

DOI: 10.33048/smzh.2024.65.513


 English version:
Siberian Mathematical Journal, 2024, 65:5, 1139–1149


© Steklov Math. Inst. of RAS, 2025