完全二阶常微分方程的奇周期解

Odd Periodic Solutions of Fully Second-Order Ordinary Differential Equations

本文讨论完全形式的二阶常微分方程-u"(t)=f(t,u(t),u’(t)),t∈R周期解的存在性,其中f:R^(3)→R连续,f(t,x,y)关于t以2π为周期.我们在非线性项f满足一些精准的不等式条件下,获得了方程奇2π-周期解的一些存在性结果.这些不等式条件允许f(t,x,y)当|(x,y)|→0及|(x,y)|→∞时关于(x,y)可以超线性或次线性增长.

This paper is concerned with the existence of periodic solutions for the fully second order ordinary differential equation-u"(t)=f(t,u(t),u’(t)),t∈R where the nonlinearity f:R^(3)→R is continuous and f(t,x,y)is 2π-periodic in t.Some existence results of odd 2π-periodic solutions are obtained under that f satisfies some precise inequality conditions.These inequality conditions allow that f(t,x,y)may be superlinear or sublinear growth on(x,y)as|(x,y)|→0 and|(x,y)l→∞.