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Yang, Qiuxia; Wang, Wanyi

Spectral properties of Sturm-Liouville operators with discontinuities at finite points. (English) Zbl 1273.34037

Math. Sci., Springer 6, Paper No. 34, 9 p. (2012).
Summary: We investigate a class of Sturm-Liouville operators with eigenparameter-dependent boundary conditions and transmission conditions at finite interior points. Our approach is based on modifying the inner product in a suitable Krein space \(K\) associated with the problem, we generate a new self-adjoint operator \(A\) such that the eigenvalues of such a problem coincide with those of \(A\). We construct its fundamental solutions, get the asymptotic formulae for its eigenvalues and fundamental solutions, discuss some properties of its spectrum, and obtain its Green function and the resolvent operator.

Cited in 5 Documents

MSC:

34B24 Sturm-Liouville theory
34L20 Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators
34L05 General spectral theory of ordinary differential operators
47E05 General theory of ordinary differential operators

Keywords:

Sturm-Liouville operator; transmission condition; eigenparameter-dependent boundary condition
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References:

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