Dirichlet-Neumann bracketing for boundary-value problems on graphs

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.

Keywords

• Differential operators
• spectrum
• graphs.