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Dependence of eigenvalues of regular Sturm-Liouville operators on the boundary condition
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In this paper, we study the continuous dependence of eigenvalue of Sturm-Liouville differential operators on the boundary condition by using of implicit function theorem. The work not only provides a new and elementary proof of the above results, but also explicitly presents the expressions for derivatives of the n-th eigenvalue with respect to given parameters. Furthermore, we obtain the new results of the position and number of the generated double eigenvalues under the real coupled boundary condition.
Xinya YANG . Dependence of eigenvalues of regular Sturm-Liouville operators on the boundary condition[J]. Frontiers of Mathematics in China, 2023 , 18(1) : 63 -74 . DOI: 10.3868/S140-DDD-023-003-X
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