Dependence of eigenvalues of regular Sturm-Liouville operators on the boundary condition

Abstract

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.

Graphical abstract

Keywords

Regular Sturm-Liouville operator / eigenvalue / implicit function theorem

References

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