边界条件含有谱参数的不连续二阶微分算子的$J$-自伴性和格林函数

Abstract

Abstract:

In this paper, the $J$ -self-adjointness and Green's function of a class of discontinuous second-order complex coefficient differential operator with eigenparameters in the boundary conditions of both endpoints are considered. By introducing a linear operator $A$ related to the problem in a suitable Hilbert space, the considered problem can be interpreted as the study of the operator in this space, and it is proved that the operator $A$ is $J$ -self-adjoint. In addition, the basic solutions of the operator and the asymptotic formula of the basic solutions are given. Furthermore, the Green's function and the resolvent operator of this operator are derived, and the asymptotic formula of Green's function is given.

Key words: second-order complex coefficient differential operator, boundary conditions, eigenparameters, $J$ -self-adjointness, Green's function

CLC Number:

O175.3

Huijie Fu, Meizhen Xu. $J$ -Self-Adjointness and Green's Function of Discontinuous Second-Order Differential Operator with Eigenparameters in the Boundary Conditions[J].Acta mathematica scientia,Series A, 2025, 45(3): 707-725.

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References 21

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$J$ -Self-Adjointness and Green's Function of Discontinuous Second-Order Differential Operator with Eigenparameters in the Boundary Conditions

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JJ-Self-Adjointness and Green's Function of Discontinuous Second-Order Differential Operator with Eigenparameters in the Boundary Conditions

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$J$ -Self-Adjointness and Green's Function of Discontinuous Second-Order Differential Operator with Eigenparameters in the Boundary Conditions