Electronic Journal of Differential Equations,
Vol. 2005(2005), No. 93, pp. 1-11.

Title: Dirichlet-Neumann bracketing for  boundary-value problems 
       on graphs

Authors: Sonja Currie (Univ. of the Witwatersrand, South Africa)
         Bruce A. Watson (Univ. of the Witwatersrand, South Africa)

Abstract: 
 We consider the spectral structure of second order boundary-value
 problems on graphs. A variational formulation for boundary-value
 problems on graphs is given. As a consequence we can formulate an
 analogue of Dirichlet-Neumann bracketing for boundary-value
 problems on graphs. This in turn gives rise to eigenvalue and
 eigenfunction asymptotic approximations.
  
Submitted March 9, 2005. Published August 24, 2005.
Math Subject Classifications: 47E05, 34L20, 34B45.
Key Words: Differential operators; spectrum; graphs.