非线性六阶周期边值问题正解的存在性与多重性  

Existence and Multiplicity of Positive Solutions to the Problems of Periodic Boundary Value for Sixth-Order ODE

作　　者：李万军[1] 

机构地区：[1]陇东学院数学与统计学院,甘肃庆阳745000

出　　处：《陇东学院学报》2012年第3期1-5,共5页Journal of Longdong University

基　　金：甘肃省高等学校研究生导师资助项目(1110-05)

摘　　要：利用锥上的不动点定理和极大值原理,研究了六阶微分方程周期边值问题正解的存在性、多重性以及无穷可解性.引入控制函数,当非线性项f(x,y)的增长速度控制在适当的有界子集内时,得到了方程一个正解、n个正解和无穷多个正解的存在性.本文还讨论了正解的不存在性.By using fixed point theorem and Maximum principles,we consider the existence of positive solutions for sixth-order differential equation with periodic boundary value,by drawing into control functions.The research showed the equation at least has one positive solution,provided the growth rates of nonlinear term are appropriate on some bounded subsets of its domain.Then the research obtained the existence results of equation has n and infinitely many positive solutions.

关 键 词：六阶两点周期边值问题 正解 锥 极大值原理 不动点定理 

分 类 号：O175.2[理学—数学]