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一类高阶左定微分算子的谱 被引量：4

Spectrum of a Class of High-order Left-definite Differential Operators
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摘要 研究了一类高阶左定微分算子的谱,利用左定微分算子与右定微分算子的关系,得到结论:自伴边界条件的高阶左定微分算子的特征值均为实数,而且上无界下无界,且算子的特征值可以排序为…λ-2λ-1λ-0<0<λ0λ1λ2… The spectrum of a class of high-order left-definite differential operators was studied.Based on the relationship between the left-definite and the right-definite operators,a conclusion is obtained.If a high-order differential operator with a self-adjoint BC is left-definite and right-indefinite,then,all its eigenvalues are real.There exist countable,infinite,positive and negative eigenvalues,and they are unbounded from below and from above,have no finite cluster point,and can be indexed to satisfy the inequality: ...λ_(-2)λ_(-1)λ_(-0)<0<λ_0λ_1λ_2...
作者 高云兰 孙炯
机构地区 内蒙古大学理工学院数学系
出处 《内蒙古大学学报（自然科学版）》 CAS CSCD 北大核心 2005年第4期367-372,共6页 Journal of Inner Mongolia University：Natural Science Edition
基金 国家自然科学基金资助项目(10261004) 高等学校博士点专项科研基金(20040126008)
关键词 高阶微分算子 左定 特征值的存在 high-order differential operators left-definite existence of eigenvalues
分类号 O175.3 [理学—基础数学]
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参考文献8

  • 1Richardson R.Contributions to the Study of Oscillatory Properties of the Solutions of Linear Differential Equations of the Second-order [J].Amer.J.Math.1918,40:283～316.
  • 2Atkinson F,Mingarelli A.Asymptotics of the Number of Zeros and of the Eigenvalues of general Weighted Sturm-Liouville Problems [J].J.Reine Angew,Math.1987,375/376:380～393.
  • 3Bennewitz C,Everitt W.On Second Order Left-Definite Boundary Value Problems [M].Uppsala:Uppsala University Department of Mathematics Report,1982.1～38.
  • 4Kong Q,Wu H,Zettl A.Left-definite Sturm-Liouville Problems [J].J.Differential Equation,2001,177:1～26.
  • 5Kong Q,Zettl A.Dependence of Eigenvalues on the Problem [J].Math.Nachr.1997,188:173～201.
  • 6Naimark M A.Linear Differential Operators [M].New York:Ungar,1968.
  • 7Leon Greenberg,Marco Marletta.Oscillation Theory and Numberical Solution of Fourth Order Sturm-Liouville Problems [J].IMA Jour.Num.Anal.1995,15:319～356.
  • 8Kong Q,Wu H,Zettl A.Singular Left-definite Sturm-Liouville Problems [J].J.Differential Equation,2004,206:1～29.

同被引文献14

  • 1Kong Q,Wu H,Zettl A, Limits of Sturm-Liouville Eigenvalues When Interval Shrinks to an end Point [J]. Royal Soc. Edinburgh Proc, A, 2007 ,to appear : 1 -20.
  • 2Kong Q,Wu H, Zettl A. Left-definite Sturm-Liouville problems [J]. Journal of Differential Equations, 2001, 177:1-26.
  • 3Eastham M S P,Kong Q,Wu H. Inequalities among eigenvalues of Sturm-Liouville problems [J]. J. Inequalities App,1999,3:25-43.
  • 4Kong Q,Wu H,Zettl A. Geometric aspects of Sturm-Liouville problems, Ⅰ. Structures on spaces of boundary conditions [J]. Royal Soc. Edinburgh Proc, 2004,130 (A) : 561-589.
  • 5Kong Q, Zettl A. Dependence of elgenvalues on the problem [J]. Math Nachr, 1997,188 : 173 - 201.
  • 6Atkinson F,Mingarelli A. A symptotics of the Number of Zeros and of the Eigenvalues of general Weighted Sturm-Liouville Problems [J]. J. Reine Angew Math, 1987,375/376: 380-393.
  • 7Kong Q ,Wu H,Zettl A. Dependence of the n-th Sturm-Liouville eigenvalue on the problem [J]. J. Differential Equations, 1999,156 : 328-354.
  • 8Richardson R. Contributions to the study of oscillatory properties of the solutions of linear differential equations of the second-order [J]. Amer J Math, 1918,40: 238-316.
  • 9Kong Qingkai. Wu Hongyou, Zettl A. Left-definte Sturm-Liouville problems [J]. J Differential Equations,2001,177: 1-26.
  • 10Kong Qingkai,Wu Hongyou,Zettl A. Singular left-definite Sturm-Liouville problems [J]. J Differential Equations,2004, 206:1-26.

引证文献4

二级引证文献3

内蒙古大学学报（自然科学版）
2005年 第4期

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