The qualitative Sturm-Liouville theory on spatial networks (Q1780358)

The authors consider boundary value problems generated by the differential expression \[ -(p(x)y')'+q(x)y=f(x) \] on the edges of a graph domain. At the pendant vertices Dirichlet boundary conditions and at the vertices of degree greater 1 the continuity conditions together with Kirchhoff-type conditions are imposed. The authors prove analogues of the Sturm comparison theorem and the Vallée-Poussin theorem (on nonoscillation criteria).