Electronic ISBN:  9781470402679 
Product Code:  MEMO/142/676.E 
List Price:  $49.00 
MAA Member Price:  $44.10 
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 142; 1999; 89 ppMSC: Primary 34; Secondary 30;
Asymptotics are built for the solutions \(y_j(x,\lambda)\), \(y_j^{(k)}(0,\lambda)=\delta_{j\,nk}\), \(0\le j,k+1\le n\) 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.
ReadershipGraduate students and research mathematicians interested in ordinary differential equations.

Table of Contents

Chapters

I. The construction of asymptotics

II. Applications: Existence and asymptotics of eigenvalues


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Asymptotics are built for the solutions \(y_j(x,\lambda)\), \(y_j^{(k)}(0,\lambda)=\delta_{j\,nk}\), \(0\le j,k+1\le n\) 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.
Graduate students and research mathematicians interested in ordinary differential equations.

Chapters

I. The construction of asymptotics

II. Applications: Existence and asymptotics of eigenvalues