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左定四阶微分算子的特征值计算

Computing Eigenvalues of Left-Definite Fourth-Order Differential Operators
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摘要 讨论了一类具有耦合边界条件的左定四阶微分算子,利用具有耦合边界条件的左定四阶微分算子和其相应的右定四阶微分算子的关系,最终给出左定四阶微分算子特征值的计算方法. In this paper, we study the left-definite regular self-adjoint differential operators with coupled boundary conditions. Using the relationship between the left-definite differen- tial operators with coupled boundary conditions and the right-definite differential operators of dimension four with coupled boundary conditions, we give an algorithm to compute eigen- values of the problems of left-definite four-order differential operators.
出处 《数学的实践与认识》 北大核心 2015年第24期279-283,共5页 Mathematics in Practice and Theory
基金 国家自然科学基金(11171295) 内蒙古工业大学科学基金(ZD201409)
关键词 微分算子 左定 右定 耦合边界条件 differential operators left-definite right-definite coupled boundary conditions
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参考文献9

  • 1Bailey P B. SLEIGN: An eigenfunction-eigenvalue code for Sturm-Liouville problem[M]. SAND 7-2044,Sandia Laboratories, Albuquerque, 1978.
  • 2Pryce J. D02KEF, NAG Library Reference Guide[M].
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  • 5张艳霞,黄振友,张学锋.左定Sturm-Liouville算子的特征值计算(英文)[J].应用泛函分析学报,2010,12(2):110-114. 被引量:2
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  • 9Kong Q, Wu H, Zettl A. Dependence of the nth Sturm-Liouville eigenvalue on the problem[J]. Journal of Differential Equations, 1999, 156(2): 328-354.

二级参考文献16

  • 1高云兰,孙炯.一类高阶左定微分算子的谱[J].内蒙古大学学报(自然科学版),2005,36(4):367-372. 被引量:4
  • 2魏广生,徐宗本.常型Sturm-Liouville问题的左定边值条件(英文)[J].数学进展,2006,35(2):191-200. 被引量:6
  • 3Bailey P B. SLEIGN: An Eigenfunction-eigenvalue Code for Sturm-Liouville Problems[M]. SAND7-2044, Sandia Laboratories, Albuquerque, 1978.
  • 4Pryce J. D02KEF, NAG Library Reference Guide[M].
  • 5Pruess S, Fulton C. Mathematical software for Sturm-Liouville problems[J]. ACM TOMS(1994), 1996, 22(4): 423-446.
  • 6Dwyer H I, Zettle A. Computing eigenvalues of regular Sturm-Liouville problems[J]. Electronic J D E, 1994, 1-10.
  • 7KONG Q, WU H, Zettl A. Left-definite Sturm-Liouville problems[J]. J Differential Equations, 2001, 177: 1-26.
  • 8Atkinson F V, Krall A M, Leaf G K, Zettl A. On the numerical computation of eigenvalues of matrix Sturm-Liouville problems with matrix coefficients[R]. Argonne National Laboratory Reports, Darien,1987.
  • 9Dwyer H I. Eigenvalues of matrix Sturm-Liouville problems with separated or coupled boundary conditions[D]. Northern Illinois University, 1993.
  • 10KONG Q, WU H, Zettl A. Dependence of the nth Sturm-Liouville problems on the boundary[J]. J Differential Equations, 1999, 156: 328-354.

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