Алгоритм побудови біфуркаційної картини нелінійної крайової задачи для рівнянь Кармана - Gromov, Vasilii A. (The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", 2017)
In the frameworks of the generalized Kantorovich method, a novel approach to detect and analyze singular points of a non-linear boundary problem for von Karman equations is proposed: an algorithm suggests that a sequence of single-dimensional boundary problems is constructed in order to solve the two-dimensional boundary problem in question. The aforesaid single-dimensional boundary problems are reduced to the equivalent Cauchy problems. In doing so, one calculates the Frechet matrix, whose degeneracy is necessary and sufficient conditions of branching. The simulation reveals the bifurcation structure for von Karman equations with the constant right term. In that case, the structure includes primary and secondary bifurcation paths.