具有转移条件的向量型Sturm-Liouville问题的特征值重数及Ambarzumyan定理

删除或更新信息，请邮件至freekaoyan#163.com(#换成@)

本站小编 Free考研考试/2021-12-27

具有转移条件的向量型Sturm-Liouville问题的特征值重数及Ambarzumyan定理刘肖云¹, 史国良², 闫军²1. 安阳工学院数理学院, 安阳 455000;
2. 天津大学数学学院, 天津 300072 On the Multiplicity of Eigenvalues of a Vectorial Sturm-Liouville Problem with Discontinuous Conditions and Related Ambarzumyan's Theorem LIU Xiaoyun¹, SHI Guoliang², YAN Jun²1. School of Mathematics and Physics, Anyang Institute of Technology, Anyang 455000, China;
2. School of Mathematics, Tianjin University, Tianjin 300072, China

摘要
图/表
参考文献
相关文章(3)
点击分布统计
下载分布统计
-->

全文: PDF(346 KB) HTML (1 KB)
输出: BibTeX | EndNote (RIS)

摘要研究了定义在有限区间内具有转移条件的m维向量型Sturm-Liouville问题.主要得到了该问题特征值重数的若干结论.证明了当矩阵值势函数Q满足一定的条件时，只能有有限个重数为m的特征值.作为重数结果的应用，证明了该问题的Ambarzumyan定理.

服务

加入引用管理器

E-mail Alert

RSS

收稿日期: 2017-08-30

PACS:

O175.3

基金资助:国家自然科学基金（11601372）资助项目.

引用本文:

刘肖云, 史国良, 闫军. 具有转移条件的向量型Sturm-Liouville问题的特征值重数及Ambarzumyan定理[J]. 应用数学学报, 2020, 43(1): 33-48. LIU Xiaoyun, SHI Guoliang, YAN Jun. On the Multiplicity of Eigenvalues of a Vectorial Sturm-Liouville Problem with Discontinuous Conditions and Related Ambarzumyan's Theorem. Acta Mathematicae Applicatae Sinica, 2020, 43(1): 33-48.

链接本文:

http://123.57.41.99/jweb_yysxxb/CN/或 http://123.57.41.99/jweb_yysxxb/CN/Y2020/V43/I1/33

[1]	Marchenko V A. Sturm-Liouville Operators and Applications. Operator Theory Advances & Applications 22, Birkhauser Verlag, 1986
[2]	Zakhariev B N, Suzko A A. Direct and inverse problems. Berlin, Heidelberg:Springer, 1990
[3]	Ahmad S, Lazer A C. On the components of extremal solutions of second order system. SIAM. J. Math. Anal., 1977, 8(1):16-23
[4]	Calvert J M, Davison W D. Oscillation theory and computational procedures for matrix SturmLiouville eigenvalue problems, with an application to the hydrogen molecular ion. J. Phys. A, 1969, 2(3):278-292
[5]	Mukhtarov O, Yakubov S. Problems for ordinary differential equations with transmission conditions. Appl. Anal., 2002, 81(5):1033-1064
[6]	Wang A P, Zettl A. Self-adjoint Sturm-Liouville problems with discontinuous boundary conditions. Methods Appl. Anal., 2015, 22(1):37-66
[7]	Ballmann W, Brin M. On the ergodicity of geodesic flows. Ergod. Theor. Dyn. Syst., 1982, 2(3-4):311-315
[8]	Kauffman R M, Zhang H K. A class of ordinary differential operators with jump boundary conditions, Evolution equations. Lecture Notes in Pure and Appl. Math., 234, Dekker, New York, 2003, 253-274
[9]	Amirov R K. On Sturm-Liouville operators with discontinuity conditions inside an interval. J. Math. Anal. Appl., 2006, 317(1):163-176
[10]	Chanane B. Eigenvalues of Sturm-Liouville problems with discontinuity conditions inside a finite interval. Appl. Math. Comput., 2007, 188(2):1725-1732
[11]	Shen C L, Shieh C T. On the multiplicity of eigenvalues of a vectorial Sturm-Liouville differential equations and some related spectral problems. Proc. Amer. Math. Soc., 1999, 127(10):2943-2952
[12]	Kong Q. Multiplicities of eigenvalues of a vector-valued Sturm-Liouville problem. Mathematika, 2002, 49(1-2):119-127
[13]	Yang C F, Huang Z Y, Yang X P. The multiplicity of spectra of a vectorial Sturm-Liouville differential equation of dimension two and some applications. Rocky Mountain J. Math., 2007, 37(4):1379-1398
[14]	Ambarzumyan V. Ueber eine frage der eigenwerttheorie. Z. Phys., 1929, 53:690-695
[15]	Yang C F, Xu X C. Ambarzumyan-type theorems on graphs with loops and double edges. J. Math. Anal. Appl., 2016, 444(2):1348-1358
[16]	Yurko V A. On Ambarzumyan-type theorems. Appl. Math. Lett., 2013, 26(4):506-509
[17]	Kıraç A A. Ambarzumyan's theorem for the quasi-periodic boundary conditions. Anal. Math. Phys., 2016, 6(3):297-300
[18]	Yang J, Yang C F. Inverse problems on the least eigenvalue. Results Math., 2014, 65(3-4):321-332
[19]	Chakravarty N K, Acharyya S K. On an extension of the theorem of V. A. Ambarzumyan. Proc. Roy. Soc. Edinburgh Sect. A, 1987, 110(1-2):79-84
[20]	Chern H H, Law C K, Wang H J. Extension of Ambarzumyan's theorem to general boundary conditions. J. Math. Anal. Appl., 2005, 309(2):764-768
[21]	Chern H H, Shen C L. On the n-dimensional Ambarzumyan's theorem. Inverse Probl., 1997, 13(1):15-18
[22]	Wang A P, Sun J, Zettl A. Two-interval Sturm-Liouville operators in modified Hilbert spaces. J. Math. Anal. Appl., 2007, 328(1):390-399
[23]	Agranovich Z S, Marchenko V A. The inverse problem of scattering theory. Gordon and Breach Science Publishers, New York-London, 1963
[24]	Boas R P. Entire functions. New York:Academic Press, 1954
[25]	Weidmann J. Spectral theory of ordinary differential operators. Lecture Notes in Mathematics 1258. Berlin:Springer Verlag, 1987
[26]	Eastham M S P. The spectral theory of periodic differential equations. Texts in Mathematics (Edinburgh). Scottish Academic Press, Edinburgh; Hafner Press, New York, 1973

[1]	孔欢欢, 王桂霞, 晴晴. 带有有限个转移条件的高阶微分算子特征函数系的完备性[J]. 应用数学学报, 2016, 39(1): 71-83.
[2]	高鹏飞, 姚斯琴, 孙炯. 边界条件中带有谱参数的不连续Sturm-Liouville算子[J]. 应用数学学报(英文版), 2012, (1): 156-167.
[3]	王桂霞, 孙炯. 带转移条件的Strum-Liouville问题特征函数的振动性[J]. 应用数学学报(英文版), 2010, 33(3): 395-411.

PDF全文下载地址:

http://123.57.41.99/jweb_yysxxb/CN/article/downloadArticleFile.do?attachType=PDF&id=14709