Branching Solutions of the Cauchy Problem for Nonlinear Loaded Differential Equations with Bifurcation Parameters

Author:

Sidorov NikolaiORCID,Sidorov DenisORCID

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.

Funder

Russian Science Foundation

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Reference21 articles.

1. A certain boundary value problem for a loaded heat equation;Dikinov;Differ. Uravn.,1976

2. On the numerical solution of loaded systems of ordinary differential equations with nonseparated multipoint and integral conditions

3. Loaded Equations and Their Applications;Nahushev,2012

4. Numerical method of solution to loaded nonlocal boundary value problems for ordinary differential equations

5. Integral Dynamical Models: Singularities, Signals Furthermore, Control;Sidorov,2015

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