Asymptotics for solutions of linear differential equations having turning points with applications Book

Asymptotics are built for the solutions $y_j(x, lambda)$, $y_j DEGREES{(k)}(0, lambda)=delta_{j, n-k}$, $0le j, k+1le n$ of the equation $L(y)=lambda p(x)y, quad xin [0,1], $ where $L(y)$ is a linear differential operator of whatever order $nge 2$ 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 $L(y)=lambda p(x)y, quad xin [0,1], $, 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