Electron. J. Diff. Eqns., Vol. 2005(2005), No. 93, pp. 1-11.

Dirichlet-Neumann bracketing for boundary-value problems on graphs

Sonja Currie, Bruce A. Watson

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.

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Sonja Currie
School of Mathematics
University of the Witwatersrand
Private Bag 3, P O WITS 2050, South Africa
email: scurrie@ananzi.co.za
Bruce A. Watson
School of Mathematics
University of the Witwatersrand
Private Bag 3, P O WITS 2050, South Africa
bwatson@maths.wits.ac.za

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