带有多项式谱参数边界条件的Sturm-Liouville问题的有限谱

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带有多项式谱参数边界条件的Sturm-Liouville问题的有限谱敖继军^1,2, 孙炯¹, 王娟²1. 内蒙古大学数学科学学院, 呼和浩特 010021;
2. 内蒙古工业大学理学院, 呼和浩特 010051 Finite Spectrum of Sturm-Liouville Problems with Boundary Conditions Polynomially Dependent on the Eigenparameter AO Jijun^1,2, SUN Jiong¹, WANG Juan²1. School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China;
2. College of Sciences, Inner Mongolia University of Technology, Hohhot 010051), China

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摘要本文研究了一类带有多项式谱参数边界条件的Sturm-Liouville问题的谱分析.通过构造，证明了这类问题具有有限谱且所有谱都是特征值.

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收稿日期: 2015-10-15

PACS:

O175.3

基金资助:国家自然科学基金（11661059，11301259，11561050）；内蒙古自然科学基金（2017JQ07）资助项目.

引用本文:

敖继军, 孙炯, 王娟. 带有多项式谱参数边界条件的Sturm-Liouville问题的有限谱[J]. 应用数学学报, 2018, 41(1): 124-133. AO Jijun, SUN Jiong, WANG Juan. Finite Spectrum of Sturm-Liouville Problems with Boundary Conditions Polynomially Dependent on the Eigenparameter. Acta Mathematicae Applicatae Sinica, 2018, 41(1): 124-133.

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[1]	Akdoǧan Z, Demirci M, Mukhtarov O Sh. Green function of discontinuous boundary-value problem with transmission conditions. Math. Meth. Appl. Sci., 2007, 30:1719-1738
[2]	Binding P A, Browne, P J, Watson B A. Sturm-Liouville problems with boundary conditions rationally dependent on the eigeparameter, Ⅱ. J. Comp. and Appl. Math., 2002, 148:147-168
[3]	Binding P A, Browne P J, Watson B A. Inverse spectral problems for Sturm-Liouville equations with eigeparameter dependent boundary conditions. J. London Math. Soc., 2000, 62(1):161-182
[4]	Collatz L. Eigenwertaufgaben mit technischen Anwendungen. Leipzig:Akad. Verlagsgesellschaft Geest & Portig, 1963
[5]	Fulton C. Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions. Proc. Roy. Soc. Edinburgh Sect. A., 1977, 77:293-308
[6]	Fulton C, Pruess S. Numerical methods for a singular eigenvalue problem with eigenparameter in the boundary conditions. J. Math. Anal. and Appl., 1979, 71:431-462
[7]	Walter J. Regular eigenvalue problems with eigenvalue parameter in the boundary conditions. Math. Z., 1973, 133:301-312
[8]	Chernozhukova A Y, Freiling G. A uniqueness theorem for inverse spectral problems depending nonlinearly on the spectral parameter. Inverse Probl. Sci. Eng., 2009, 17:777-785
[9]	Freiling G, Yurko V A. Inverse problems for Sturm-Liouville equations with boundary conditions polynomially dependent on the spectral parameter. Inverse Probl., 2010, 26:055003, 17pp
[10]	Yokus N, Koprubasi T. Spectrum of the Sturm-Liouville operators with boundary conditions polynomially dependent on the spectral parameter. J. Inequal. Appl., 2015, 42:8pp
[11]	Tretter Ch. Boundary eigenvalue problems with differential equations Nη=λPη with λ-polynomial boundary conditions. J. Differ. Equ., 2001, 170:408-471
[12]	Atkinson F V. Discrete and Continuous Boundary Problems. New York, London:Academic Press, 1964
[13]	Kong Q, Wu H, Zettl A. Sturm-Liouville problems with finite spectrum. J. Math. Anal. Appl., 2001, 263:748-762
[14]	Kong Q, Volkmer H, Zettl A. Matrix representations of Sturm-Liouville problems with finite spectrum. Result. Math., 2009, 54:103-116
[15]	Ao J J, Sun J, Zhang M Z. The finite spectrum of Sturm-Liouville problems with transmission conditions. Appl. Math. Comput., 2011, 218:1166-1173
[16]	Ao J J, Sun J, Zhang M Z. The finite spectrum of Sturm-Liouville problems with transmission conditions and eigenparameter-dependent boundary conditions. Result. Math., 2013, 63:1057-1070
[17]	Ao J J, Bo F Z, Sun J. Fourth order boundary value problems with finite spectrum. App. Math. Comput., 2014, 244:952-958
[18]	Ao J J, Sun J, Zettl A. Finite spectrum of 2nth order boundary value problems. Appl. Math. Lett., 2015, 42:1-8
[19]	Bo F Z, Ao J J. The finite spectrum of fourth order boundary value problems with transmission conditions. Abstr. Appl. Anal., 2014 Article ID 175489, 7 pages
[20]	Everitt W N, Race D. On necessary and sufficient conditions for the existence of Caratheodory solutions of ordinary differential equations. Quaest. Math., 1976, 3:507-512
[21]	Zettl A. Sturm-Liouville Theory. In:Mathematical Surveys and Monographs, 121, Amer. Math. Soc., Providence RI, 2005

[1]	王忠, 张鹏军, 曹玉峰. 边界条件中带有谱参数且在多个点不连续的Sturm-Liouville算子的特征问题[J]. 应用数学学报, 2016, 39(4): 505-522.

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