基于Wazewski拓扑原理的非自治非线性系统V-有界解的存在性
Existence of V-bounded solutions for nonautonomous nonlinear systems via the Wazewski topological principle
摘要：
利用Wazewski拓扑原理建立了非线性非自治系统整体（定义在整个时间轴上）解存在的若干新的充分条件.所考虑的系统的特点是由单调性相对于一个特定的辅助指导功能W（t，x）取决于时间和相位坐标。另一个辅助空间强制函数V（t，x）被用来估计整体解在扩展相空间中的位置。开发的方法适用于拉格朗日系统，特别是建立新的充分条件存在的殆周期解。
英文摘要：
We establish a number of new sufficient conditions for the existence of global (defined on the entire time axis) solutions of nonlinear nonautonomous systems by means of the Wazewski topological principle. The systems under consideration are characterized by the monotonicity property with respect to a certain auxiliary guiding function W(t,x) depending on time and phase coordinates. Another auxiliary spatially coercive function V(t,x) is used to estimate the location of global solutions in the extended phase space. The approach developed is applied to Lagrangian systems, and in particular, to establish new sufficient conditions for the existence of almost periodic solutions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
