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Asymptotics for Solutions of Linear Differential Equations Having Turning Points with Applications

S. Strelitz University of Haifa, Haifa, Israel
Available Formats:
Electronic ISBN: 978-1-4704-0267-9
Product Code: MEMO/142/676.E
List Price: $49.00 MAA Member Price:$44.10
AMS Member Price: $29.40 Click above image for expanded view Asymptotics for Solutions of Linear Differential Equations Having Turning Points with Applications S. Strelitz University of Haifa, Haifa, Israel Available Formats:  Electronic ISBN: 978-1-4704-0267-9 Product Code: MEMO/142/676.E  List Price:$49.00 MAA Member Price: $44.10 AMS Member Price:$29.40
• Book Details

Memoirs of the American Mathematical Society
Volume: 1421999; 89 pp
MSC: Primary 34; Secondary 30;

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.

Graduate students and research mathematicians interested in ordinary differential equations.

• Chapters
• I. The construction of asymptotics
• II. Applications: Existence and asymptotics of eigenvalues
• Requests

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Volume: 1421999; 89 pp
MSC: Primary 34; Secondary 30;

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.