The existence and properties of the solution of a class of nonlinear differential equations with switching at variable times
Copyright policy )The existence and properties of the solution of a class of nonlinear differential equations with switching at variable times
<p style='text-indent:20px;'>In this paper, we deal with the qualitative theory for a class of nonlinear differential equations with switching at variable times (SSVT), such as the existence and uniqueness of the solution, the continuous dependence and differentiability of the solution with respect to parameters and the stability. Firstly, we obtain the existence and uniqueness of a global solution by defining a reasonable solution (see Definition 2.1). Secondly, the continuous dependence and differentiability of the solution with respect to the initial state and the switching line are investigated. Finally, the global exponential stability of the system is discussed. Moreover, we give the necessary and sufficient conditions of SSVT just switching <inline-formula><tex-math id="M1">\begin{document}$ k\in \mathbb{N} $\end{document}</tex-math></inline-formula> times on bounded time intervals.</p>
- Guizhou University China (People's Republic of)
Nonautonomous smooth dynamical systems, existence, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, uniqueness, switching at variable times, Discontinuous ordinary differential equations, Stability of solutions to ordinary differential equations, Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations, stability, Global stability of solutions to ordinary differential equations, Asymptotic properties of solutions to ordinary differential equations, continuous dependence, switched systems, differentiability
Nonautonomous smooth dynamical systems, existence, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, uniqueness, switching at variable times, Discontinuous ordinary differential equations, Stability of solutions to ordinary differential equations, Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations, stability, Global stability of solutions to ordinary differential equations, Asymptotic properties of solutions to ordinary differential equations, continuous dependence, switched systems, differentiability
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