NEW CANONICAL FORMS OF SELF-ADJOINT BOUNDARY CONDITIONS FOR REGULAR DIFFERENTIAL OPERATORS OF ORDER FOUR

Qinglan Bao; Jiong Sun; Xiaoling Hao; Anton Zettl

doi:10.11948/20180343

2019 Volume 9 Issue 6

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Article navigation > Journal of Applied Analysis & Computation > 2019 > 9(6): 2190-2211

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Qinglan Bao, Jiong Sun, Xiaoling Hao, Anton Zettl. NEW CANONICAL FORMS OF SELF-ADJOINT BOUNDARY CONDITIONS FOR REGULAR DIFFERENTIAL OPERATORS OF ORDER FOUR[J]. Journal of Applied Analysis & Computation, 2019, 9(6): 2190-2211. doi: 10.11948/20180343

Citation:

Qinglan Bao, Jiong Sun, Xiaoling Hao, Anton Zettl. NEW CANONICAL FORMS OF SELF-ADJOINT BOUNDARY CONDITIONS FOR REGULAR DIFFERENTIAL OPERATORS OF ORDER FOUR[J]. Journal of Applied Analysis & Computation, 2019, 9(6): 2190-2211. doi: 10.11948/20180343

NEW CANONICAL FORMS OF SELF-ADJOINT BOUNDARY CONDITIONS FOR REGULAR DIFFERENTIAL OPERATORS OF ORDER FOUR

1.
Math., Dept., Inner Mongolia University, Hohhot, 010021, China
2.
Math. Dept., Northern Illinois University, DeKalb, Il. 60115, USA

Corresponding author: Email address: zettl@msn.com (A. Zettl)

Abstract

Abstract

In this paper, we find new canonical forms of self-adjoint boundary conditions for regular differential operators of order two and four. In the second order case the new canonical form unifies the coupled and separated canonical forms which were known before. Our fourth order forms are similar to the new second order ones and also unify the coupled and separated forms. Canonical forms of self-adjoint boundary conditions are instrumental in the study of the dependence of eigenvalues on the boundary conditions and for their numerical computation. In the second order case this dependence is now well understood due to some surprisingly recent results given the long history and voluminous literature of Sturm-Liouville problems. And there is a robust code for their computation: SLEIGN2.
- Differential operators /
- boundary conditions /
- self-adjoint /
- canonical forms
MSC: 34B24, 34L15, 34B08, 34L05

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References

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