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

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.