Rocky Mountain Journal of Mathematics

Asymptotics of the eigenvalues of self-adjoint fourth order differential operators with separated eigenvalue parameter dependent boundary conditions

Manfred Möller and Bertin Zinsou

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Abstract

In this paper, an eigenvalue problem for a regular fourth order ordinary differential equation is considered, where one of the boundary conditions linearly depends upon the eigenvalue parameter. The first four terms in the asymptotic expansion of the eigenvalues are derived.

Article information

Source
Rocky Mountain J. Math., Volume 47, Number 6 (2017), 2013-2042.

Dates
First available in Project Euclid: 21 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1511254962

Digital Object Identifier
doi:10.1216/RMJ-2017-47-6-2013

Mathematical Reviews number (MathSciNet)
MR3725254

Zentralblatt MATH identifier
1381.34042

Subjects
Primary: 34B07: Linear boundary value problems with nonlinear dependence on the spectral parameter 34B08: Parameter dependent boundary value problems 34B09: Boundary eigenvalue problems 34L20: Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions

Keywords
Fourth order differential operators self-adjoint boundary conditions eigenvalue distribution pure imaginary eigenvalues asymptotics of eigenvalues

Citation

Möller, Manfred; Zinsou, Bertin. Asymptotics of the eigenvalues of self-adjoint fourth order differential operators with separated eigenvalue parameter dependent boundary conditions. Rocky Mountain J. Math. 47 (2017), no. 6, 2013--2042. doi:10.1216/RMJ-2017-47-6-2013. https://projecteuclid.org/euclid.rmjm/1511254962


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References

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