二阶隐式微分方程周期边值问题的上下解与迭合度

Upper and lower solutions of second order implicit differential equation with periodic boundary value problems and coincidence degree

利用上下解方法和迭合度理论,讨论了二阶隐式微分方程周期边值问题(x″(t)=f(t,x(t),x″(t)),t∈[0,2π],x(0)=x(2π),x′(0)=x′(2π))解的存在性,其中f:[0,2π]×R^2→R连续,获得了至少存在一个解的充分条件。

By using upper and lower solutions method and coincidence degree theory,the existence of solutions for a second-order implicit differential equation with periodic boundary value problems （x″（t）=f（t,x（t）,x″（t））,t∈[0,2π],x（0）=x（2π）,x′（0）=x′（2π）） is discussed,where f：[0,2π]×R^2→R is continuous.An existence result that there is at least one solution is obtained.The effectiveness of the result is proved by using an example.