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

Juan Pablo Pinasco

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 x+λq(t)x=0 on an infinite interval [a,+). 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.