×

The analogue of the formula of integration by parts on geometric graph. (Russian. English summary) Zbl 1401.26022

Summary: In this paper, the integration by parts formula is extended for an integral in which the integration is carried out along the geometric graph. The need for integration by parts arises, for example, in the modeling of deformations and oscillatory processes of objects located along a geometric graph. The proven formula makes it possible to obtain mathematical models describing different processes on the graph. In this case, the resulting models are realized in the form of differential equations, defined pointwise, and supplemented by boundary conditions. That conception (pointwise given differential equation), formulated by Yu. V. Pokorny, showed its effectiveness for differential equations of the second and fourth orders on the interval.

MSC:

26A42 Integrals of Riemann, Stieltjes and Lebesgue type
PDFBibTeX XMLCite