A dissipative third-order boundary value problem with distributional potentials and eigenparameter-dependent boundary conditions

Fei-fan Li; Ji-jun Ao; Fei-fan Li; Ji-jun Ao

doi:10.3934/era.2025149

Electronic Research Archive

2025, Volume 33, Issue 5: 3378-3393. doi: 10.3934/era.2025149

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Research article

A dissipative third-order boundary value problem with distributional potentials and eigenparameter-dependent boundary conditions

Fei-fan Li ,
Ji-jun Ao ^,

College of Sciences, Inner Mongolia University of Technology, Hohhot 010051, China

Received: 27 December 2024 Revised: 08 May 2025 Accepted: 23 May 2025 Published: 29 May 2025

This paper investigates a class of dissipative boundary value problems arising from a third-order differential equation with distributional potentials and eigenparameter-dependent boundary conditions. Initially, we transform the boundary value problem into the corresponding operator problem. We then demonstrate that the operator is dissipative and examine certain eigenvalue properties of the operator. Furthermore, by applying Krein's theorem, we establish the completeness theorems for both the boundary value problem and the corresponding operator.
- third-order boundary value problem,
- dissipative differential operator,
- distributional potentials,
- completeness theorems
Citation: Fei-fan Li, Ji-jun Ao. A dissipative third-order boundary value problem with distributional potentials and eigenparameter-dependent boundary conditions[J]. Electronic Research Archive, 2025, 33(5): 3378-3393. doi: 10.3934/era.2025149

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Abstract

This paper investigates a class of dissipative boundary value problems arising from a third-order differential equation with distributional potentials and eigenparameter-dependent boundary conditions. Initially, we transform the boundary value problem into the corresponding operator problem. We then demonstrate that the operator is dissipative and examine certain eigenvalue properties of the operator. Furthermore, by applying Krein's theorem, we establish the completeness theorems for both the boundary value problem and the corresponding operator.

References

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