不同特征值对应的特征向量正交。 Thm 2.7(Spectral theorem 谱定理) 若T是H上一个自伴随的紧算子, 则存在H上的一组标准正交基{φk}k=1∞, 其中每个φk都是T的一个特征向量,即$$T\varphi_k=\lambda_k \varphi_k.$$ 特别的,每个λk都是实数,且λ→0ask→∞. Back to Sturm-Liouville 考虑以下集合...
This chapter discusses Sturm-Liouville theory. The chapter discusses differential equation; existence, uniqueness, and bounds for Solutions; boundary problem; oscillatory properties; interpolatory property; eigenfunction expansion; second-order equation with discontinuities; Green's function; and convergence of...
Norrie Everitt The Titchmarsh-Weyl Eigenfunction Expansion Theorem for Sturm-Liouville Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 Victor A. Galaktionov and Petra J. Harwin Sturm’s Theorems on Zero Sets in Nonlinear ...
muchoftheSturm-LiouvilletheoryisessentiallythetheorywedevelopedforHermitian/self-adjointoperatorsinchapter7,withourbig“Sturm-Liouvilletheorems”beingreminiscentofthe“BigTheoremonHermitianOperators”,theorem7.8onpage7–19.Bytheway,youshouldbeawarethatthefirstboundary-valueproblemforwhicha“Sturm-Liouvilletheory”...
《Sturm-Liouville问题的几何结构（英文版）》是2019年科学出版社出版的图书，作者是傅守忠、王忠、吴宏友。内容简介 本书从几何的角度去研究Sturm-Liouville问题的谱，将边界条件可化为解析流形（如正则自伴边条件形成一个4维的紧解析流形），将所有是Sturm-Liouville问题放在一起形成一个空间。在该空间赋予一定的拓扑...
In Sturm-Liouville Theory: Past and Present (W. Amrein, A. Hinz and D. Pearson. eds.), pp. ... B Simon - Birkhäuser Basel 被引量: 67发表: 2005年 The Titchmarsh-Weyl Eigenfunction Expansion Theorem for Sturm-Liouville Differential Equations N. Everitt, The Titchmarsh-Weyl eigenfunction ...
Sturm-Liouville Theory and its Applications 2024 pdf epub mobi 电子书 图书描述 Provides a rigorous introduction to Sturm-Liouville theory at a level suitable for undergraduates Includes clearly worked examples and exercises with solutions, making the book well suited for self-study Meets the needs of...
Sturm-Liouville边值问题论文:几类非线性微分方程的正解Sturm-Liouville边值问题奇异格林函 数不动点指数定理正解Sturm-Liouville边值问题论文:几类非线性微分方程的正解【中文摘要】近年来,随着科学技术的进步,物理技术和应用数学的不断发展,各种各样的非线性问题日益涌现.这些非线性问题日益引起了人们的广畸捅扶咀恨...
In this survey paper some new developments of Sturm-Liouville theory in recent three decades are outlined and reviewed. 综合评述了Sturm-Liouville理论在近 30年内的若干新发展,主要内容包括如下4个方面:1 由拟导数所生成的微分算子;2 常微分算子自伴性的完全解析描述;3 带权函数的Sturm-Liouville问题(包括...
sturm-liouville问题特征值间的不等式 Sturm-Liouville equation is a second-order linear differential equation that has applications in various fields, including mathematical physics, engineering, and quantum mechanics. The equation can be written as: -(p(x)y')'+q(x)y=λr(x)y where p(x), q...