International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 29895, 7 pages
The distribution of nonprincipal eigenvalues of singular
second-order linear ordinary differential equations
Instituto de Ciencias, Universidad Nacional de General Sarmiento, J. M. Gutierrez 1150, Los Polvorines, Buenos Aires 1613, Argentina
Received 21 February 2005; Accepted 27 July 2006
Copyright © 2006 Juan Pablo Pinasco. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We obtain the asymptotic distribution of the nonprincipal eigenvalues
associated with the singular problem on an infinite interval
. Similar to the regular eigenvalue problem on compact intervals, we can
prove a Weyl-type expansion of the eigenvalue counting function, and we derive the
asymptotic behavior of the eigenvalues.