Geodesic
Nonclassical Sturm-Liouville problems and Schrödinger operators on radial trees
Electronic Journal of Differential Equations, Tome 2000 (2000).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Schrodinger operators on graphs with weighted edges may be defined using possibly infinite systems of ordinary differential operators. This work mainly considers radial trees, whose branching and edge lengths depend only on the distance from the root vertex. The analysis of operators with radial coefficients on radial trees is reduced, by a method analogous to separation of variables, to nonclassical boundary-value problems on the line with interior point conditions. This reduction is used to study self adjoint problems requiring boundary conditions `at infinity'.
Classification : 34B10, 47E05
Keywords: Schrödinger operators on graphs, graph spectral theory, boundary-value problems, interior point conditions 
@article{EJDE_2000__2000__a122,
     author = {Carlson, Robert},
     title = {Nonclassical {Sturm-Liouville} problems and {Schr\"odinger} operators on radial trees},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2000},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a122/}
}
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Carlson, Robert. Nonclassical Sturm-Liouville problems and Schrödinger operators on radial trees. Electronic Journal of Differential Equations, Tome 2000 (2000). http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a122/