Memoirs of the American Mathematical Society 1999; 89 pp; softcover Volume: 142 ISBN10: 0821813528 ISBN13: 9780821813522 List Price: US$49 Individual Members: US$29.40 Institutional Members: US$39.20 Order Code: MEMO/142/676
 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. Readership Graduate students and research mathematicians interested in ordinary differential equations. Table of Contents  The construction of asymptotics
 Application: Existence and asymptotics of eigenvalues
