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Asymptotics for Solutions of Linear Differential Equations Having Turning Points with Applications
S. Strelitz, University of Haifa, Israel
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Memoirs of the American Mathematical Society
1999; 89 pp; softcover
Volume: 142
ISBN-10: 0-8218-1352-8
ISBN-13: 978-0-8218-1352-2
List Price: US$46
Individual Members: US$27.60
Institutional Members: US$36.80
Order Code: MEMO/142/676
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Asymptotics are built for the solutions \(y_j(x,\lambda)\), \(y_j^{(k)}(0,\lambda)=\delta_{j\,n-k}\), \(0\le j,k+1\le n\) of the equation \[L(y)=\lambda p(x)y,\quad x\in [0,1], \qquad\qquad\qquad(1)\] where \(L(y)\) is a linear differential operator of whatever order \(n\ge 2\) and \(p(x)\) is assumed to possess a finite number of turning points. The established asymptotics are afterwards applied to the study of:

1) the existence of infinite eigenvalue sequences for various multipoint boundary problems posed on Equation (1), especially as \(n=2\) and \(n=3\) (let us be aware that the same method can be successfully applied on many occasions in case \(n>3\) too) and

2) asymptotical distribution of the corresponding eigenvalue sequences on the complex plane.

Readership

Graduate students and research mathematicians interested in ordinary differential equations.

Table of Contents

  • The construction of asymptotics
  • Application: Existence and asymptotics of eigenvalues
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