| eBook 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 |
| eBook 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 DetailsMemoirs of the American Mathematical SocietyVolume: 142; 1999; 89 ppMSC: Primary 34; Secondary 30
Asymptotics are built for the solutions \(y_j(x,\lambda)\), \(y_j^{(k)}(0,\lambda)=\delta_{j\,n-k}\), \(0\le j,k+1\le n\) 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.
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
-
-
RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Requests
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
