边界条件和转移条件均含谱参数的二阶J-对称微分算子
Second-Order J-Symmetric Differential Operators with Eigenparameter-Dependent Boundary and Transmission Conditions
DOI: 10.12677/aam.2025.141037, PDF,    国家自然科学基金支持
作者: 付慧洁, 许美珍*：内蒙古工业大学理学院，内蒙古 呼和浩特
关键词: 二阶复系数微分算子；谱参数；J-自伴性；格林函数；Second-Order Complex Coefficient Differential Operator； Eigenparameter； J-Self-Adjointness； Green’s Function
摘要: 考虑一类耦合边界条件和转移条件均含谱参数的二阶复系数微分算子的J-自伴性和格林函数。在适当的Hilbert空间上定义一个与问题相关的线性算子，将所研究的问题转化为对此空间中算子的研究，并证明该算子是J-自伴的。另外，通过构造微分方程的基本解得到问题的格林函数。
Abstract: In this paper, we consider the J-self-adjointness and Green’s function of a class of discontinuous second-order complex coefficient differential operator with eigenparameters in boundary and transmission conditions. By introducing a linear operator 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 this operator is proved to be J-self-adjoint. In addition, the Green’s function of the problem is obtained by constructing the fundamental solutions of the differential equation.
文章引用：付慧洁, 许美珍. 边界条件和转移条件均含谱参数的二阶J-对称微分算子[J]. 应用数学进展, 2025, 14(1): 374-385. https://doi.org/10.12677/aam.2025.141037

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