Research Article

On a class of third-order dissipative differential operator with distributional potentials

Published in: Quaestiones Mathematicae
Volume 48 , issue 2 , 2025 , pages: 331–344

DOI: 10.2989/16073606.2024.2395377

Author(s): Ji-jun Ao Inner Mongolia University of Technology, China , Fei-fan Li Inner Mongolia University of Technology, China

Keywords: Primary: 34L10 , 34B05 , Secondary: 47A45 , Third-order boundary value problem , dissipative differential operator , distributional potentials , completeness theorems

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Abstract

This paper aims to investigate a class of boundary value problems generated by a third-order differential equation with distributional potentials and some dissipative boundary conditions. We first construct an operator related to the problem, then prove that the operator is dissipative and show some eigenvalue properties of this operator. Further using Krein’s theorem we prove the completeness theorems of the operator.

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