Geodesic
Solvability of the Boundary-Value Problem
Matematičeskie zametki, Tome 80 (2006) no. 1, pp. 60-68

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The solvability of the boundary-value problem for a string-beam model is studied. The model is described by an equation of orders 2 and 4 on different edges of an arbitrary graph. Criteria for the problem to be degenerate and nondegenerate are obtained; in particular, it is proved that the nondegeneracy of the problem is equivalent to the maximum principle.
Keywords: geometric graph (network), ordinary differential equation on a graph, boundary-value problem, nondegeneracy, degeneracy, maximum principle. 
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     author = {K. P. Lazarev and T. V. Beloglazova},
     title = {Solvability of the {Boundary-Value} {Problem}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {60--68},
     publisher = {mathdoc},
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     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2006_80_1_a7/}
}
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K. P. Lazarev; T. V. Beloglazova. Solvability of the Boundary-Value Problem. Matematičeskie zametki, Tome 80 (2006) no. 1, pp. 60-68. http://geodesic.mathdoc.fr/item/MZM_2006_80_1_a7/