A class of dissipative differential operators of order three

Tao Wang; Jijun Ao; Anton Zettl; Tao Wang; Jijun Ao; Anton Zettl

doi:10.3934/math.2021412

AIMS Mathematics

2021, Volume 6, Issue 7: 7034-7043. doi: 10.3934/math.2021412

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Research article

A class of dissipative differential operators of order three

1.
College of Sciences, Inner Mongolia University of Technology, Hohhot 010051, China
2.
Mathematics Department, Northern Illinois University, DeKalb, IL. 60115, USA

Received: 27 October 2020 Accepted: 18 April 2021 Published: 26 April 2021
MSC : 34B20, 34L10, 47A48

In this paper we find a class of boundary conditions which determine dissipative differential operators of order three and prove that these operators have no real eigenvalues. The completeness of the system of eigenfunctions and associated functions is also established.
- third order boundary value problems,
- dissipative operators,
- eigenvalues,
- limit circle case
Citation: Tao Wang, Jijun Ao, Anton Zettl. A class of dissipative differential operators of order three[J]. AIMS Mathematics, 2021, 6(7): 7034-7043. doi: 10.3934/math.2021412

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Abstract

In this paper we find a class of boundary conditions which determine dissipative differential operators of order three and prove that these operators have no real eigenvalues. The completeness of the system of eigenfunctions and associated functions is also established.

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