학술논문
Branching Solutions of the Cauchy Problem for Nonlinear Loaded Differential Equations with Bifurcation Parameters.
Document Type
Article
Author
Source
Subject
*NONLINEAR differential equations
*NONLINEAR equations
*STIELTJES integrals
*INTEGRAL equations
*
*
*
Language
ISSN
2227-7390
Abstract
The Cauchy problem for a nonlinear system of differential equations with a Stieltjes integral (loads) of the desired solution is considered. The equation contains bifurcation parameters where the system has a trivial solution for any values. The necessary and sufficient conditions are derived for those parameter values (bifurcation points) in the neighborhood of which the Cauchy problem has a non-trivial real solution. The constructive method is proposed for the solution of real solutions in the neighborhood of those points. The method uses successive approximations and builds asymptotics of the solution. The theoretical results are illustrated by example. The Cauchy problem with loads and bifurcation parameters has not been studied before. [ABSTRACT FROM AUTHOR]