On a class of ordinary differential equations of various orders on a graph
The authors consider the Sturm-Liouville problem \((pu'')''- (qu')'= f\), \(u_{| \partial\Gamma}= 0\), with some stress balance condition, where \(\Gamma\) is a system of bars and strings with a cycle. They prove the solvability of the problem under consideration and derive some properties of the solution, such as the sign, the sign of the Green function, and some results on the corresponding spectral problem.
scientific article; zbMATH DE number 2115586