非线性微分系统解的有界性和周期解的存在性

Boundedness of Solutions and Existence of Periodic Solutions of Nonlinear Differential Equations

中文关键词:  非线性  有界性  周期解

英文关键词:Nonlinear  boundedness  periodic solution.

中文摘要:

      本文运用了比较新的手法,证明了非线性微分系统(dx)/(dt)=1/(a(x))[c(y)-b(x)];(dy)/(dt)=-a(x)[h(x)-e(t)](1)(其中a(x),b(x),h(x),c(y),e(t)为连续可微函数,x,y∈R,t∈[0,+∞),且a(x)>0)解的有界性及周期解的存在性,并应用该结论讨论了强迫振动方程:x+(f(x)+g(x)x)x+h(x)=e(t)(2)(其中f(x),g(x)为连续可微函数,x∈R,h(x),e(t)同上)解的有界性及周期解的存在性.

英文摘要:

      In this paper, we used a new method to discuss the boundedness and existence of periodic solutions of nonlinear differential system (dx)/(dt)=1/(a(x))[c(y)-b(x)];(dy)/(dt)=-a(x)[h(x)-e(t)] and applied these conclusions to study the boundedness of solutions and the existence of periodic solutions of the forcing vibrating differential equations x+(f(x)+g(x)x)x+h(x)=e(t).