International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 14, Article ID 29895, 7 pages
doi:10.1155/IJMMS/2006/29895

The distribution of nonprincipal eigenvalues of singular second-order linear ordinary differential equations

Abstract

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.