Boundary estimates for solutions of non-homogeneous boundary value problems on graphs

Authors:
Sonja Currie;Bruce A. Watson
Affiliations:
University of the Witwatersrand, School of Mathematics, South Africa;University of the Witwatersrand, School of Mathematics, South Africa
Venue:
MATH'07 Proceedings of the 12th WSEAS International Conference on Applied Mathematics
Year:
2007

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Eigenvalue asymptotics for differential operators on graphs

Journal of Computational and Applied Mathematics

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Abstract

We consider the Sturm-Liouville operator on a graph and give bounds for the norms of the boundary values of solutions to the non-homogeneous boundary value problem in terms of the norm of the non-homogeneity. In addition the eigenparameter dependence of these bounds is studied.