无穷区间上带有积分边值分数阶微分方程的多个正解的存在性  

EXISTENCE OF POSITIVE SOLUTIONS FOR A CLASS OF FRACTIONAL DIFFERENTIAL EQUATIONS WITH INTEGRAL BOUNDARY VALUE CONDITION ON AN INFINITE INTERVAL

作　　者：郭丽敏[1,2] 张兴秋[3,2] 

机构地区：[1]曲阜师范大学数学科学学院,曲阜273165 [2]聊城大学数学科学学院,聊城252059 [3]济宁医学院医学信息工程学院,济宁272067

出　　处：《系统科学与数学》2014年第6期752-762,共11页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(11371221;11071141);山东省优秀中青年科学家奖励基金(BS2010SF004);山东省高等学校科技发展计划(J1OLA53)资助课题

摘　　要：通过讨论Green函数的性质并构造特殊的锥,利用Leggett-Williams不动点定理研究了无穷区间上带有积分边值的分数阶微分方程多个正解的存在性.最后给出了一个例子说明了所得结果的正确性.By studying the properties of Green function, a special cone is constructed to establish the existence of multiple positive solutions for fractional differential equation with integral boundary value conditions by using Leggett-Williams fixed point theorem on an infinite interval. Finally, an example is given to illustrate the effectiveness of the results.

关 键 词：分数阶微分方程 积分边值 无穷区间 锥 Leggett—Williams不动点定理 

分 类 号：O175.8[理学—数学]