SPECTRAL PROPERTIES OF STURM-LIOUVILLE OPERATORS WITH DISCONTINUITIES AT FINITE POINTS

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YANG QIUXIA; WANG WANYI

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Journal Paper

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Journal: MATHEMATICAL SCIENCES Year:2012 | Volume:6 | Issue:- Page(s): 1-9

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Title

SPECTRAL PROPERTIES OF STURM-LIOUVILLE OPERATORS WITH DISCONTINUITIES AT FINITE POINTS

Author(s)

YANG QIUXIA | WANG WANYI | Issue Writer Certificate

Keywords

STURM-LIOUVILLE OPERATOR

TRANSMISSION CONDITION

EIGENPARAMETER-DEPENDENT BOUNDARY CONDITION

Abstract

Purpose: In this paper, we investigate a class of STURM-LIOUVILLE OPERATORs with EIGENPARAMETER-DEPENDENT BOUNDARY CONDITIONs and TRANSMISSION CONDITIONs at finite interior points.Methods: By 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.Results: 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.Conclusions: Three important conclusions can be drawn: (1) the new operator A is self-adjoint in the Krein space K; (2) if θi>0, i=1, m-, and ρj>0, j=1, 2, then, the eigenvalues of the problem (Equations 1 to 5) are analytically simple; (3) the residual spectrum of the operator A is empty, i.e., σr (A)=∅.

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APA: Copy

YANG, QIUXIA, & WANG, WANYI. (2012). SPECTRAL PROPERTIES OF STURM-LIOUVILLE OPERATORS WITH DISCONTINUITIES AT FINITE POINTS. MATHEMATICAL SCIENCES, 6(-), 1-9. SID. https://sid.ir/paper/322599/en

Vancouver: Copy

YANG QIUXIA, WANG WANYI. SPECTRAL PROPERTIES OF STURM-LIOUVILLE OPERATORS WITH DISCONTINUITIES AT FINITE POINTS. MATHEMATICAL SCIENCES[Internet]. 2012;6(-):1-9. Available from: https://sid.ir/paper/322599/en

IEEE: Copy

QIUXIA YANG, and WANYI WANG, “SPECTRAL PROPERTIES OF STURM-LIOUVILLE OPERATORS WITH DISCONTINUITIES AT FINITE POINTS,” MATHEMATICAL SCIENCES, vol. 6, no. -, pp. 1–9, 2012, [Online]. Available: https://sid.ir/paper/322599/en

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