Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 123, pp. 1-13.

Title: Sturm-Liouville eigenvalue characterizations
  
Authors: Paul B. Bailey  (Tucson, AZ, USA)
         Anton Zettl (Northern Illinois Univ., DeKalb, IL, USA)
	 
Abstract:
 We study the relationship between the eigenvalues of separated self-adjoint
 boundary conditions and coupled self-adjoint conditions. Given an arbitrary
 real coupled boundary condition determined by a coupling matrix K we
 construct a one parameter family of separated conditions and show that all
 the eigenvalues for K and -K are extrema of the eigencurves of this family.
 This characterization makes it possible to use the well known Prufer
 transformation which has been used very successfully, both theoretically and
 numerically, for separated conditions, also in the coupled case. In
 particular, this characterization makes it possible to compute the
 eigenvalues for any real coupled self-adjoint boundary condition using any
 code which works for separated conditions.

Submitted June 4, 2012. Published July 23, 2012.
Math Subject Classifications: 05C38, 15A15, 05A15, 15A18
Key Words: Sturm-Liouville problems; computing eigenvalues; 
           separated and coupled boundary conditions.