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

作　　者：王丽[1] 刘永莉[1] 李永军[1] 霍锦霞[1] 

机构地区：[1]兰州城市学院数学学院,甘肃兰州730070

出　　处：《高校应用数学学报（A辑）》2013年第3期329-334,共6页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11261027;11161026)

摘　　要：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.

关 键 词：隐式微分方程 周期边值问题 上下解 迭合度 存在性 

分 类 号：O175.8[理学—数学]