On the Nonclassical Asymptotics of the Eigenvalues of a Boundary Value Problem for a Second-Order Differential-Operator Equation

• Published in: Differential equations Vol. 58; no. 12; pp. 1571 - 1578
• Main Author: Aliev, B. A.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01-12-2022; Springer; Springer Nature B.V
• Subjects: Asymptotic properties; Boundary conditions; Boundary value problems; Difference and Functional Equations; Differential equations; Eigenvalues; Hilbert space; Mathematics; Mathematics and Statistics; Operators (mathematics); Ordinary Differential Equations; Partial Differential Equations
• ISSN: 0012-2661; 1608-3083
• DOI: 10.1134/S00122661220120011

In a separable Hilbert space
, we study the asymptotic behavior of the eigenvalues of a boundary value problem for a second-order differential-operator equation. The spectral parameter of the problem occurs linearly in the equation and as a quadratic trinomial in one of the boundary conditions. Asymptotic formulas for the eigenvalues of the problem are found.