A class of fourth-order differential equations on a spatial net. (English. Russian original) Zbl 0891.34018
Dokl. Math. 52, No. 3, 433-435 (1995); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 345, No. 6, 730-732 (1995).
The fourth-order differential equation
\[
(p(x)y'')''-(q(x)y')'=f(x)
\]
is considered on a spatial net. At the interior nodes of the net, interface conditions have to be satisfied, and boundary conditions are given at the boundary vertices. The authors state properties of the Green function for this problem and give necessary and sufficient conditions for the unique solvability of this problem.
Reviewer: M.Möller (Regensburg)
MSC:
| 34B10 | Nonlocal and multipoint boundary value problems for ordinary differential equations |
| 34B27 | Green’s functions for ordinary differential equations |
