具Caputo导数分数阶微分方程边值问题正解的存在性  

Existence of positive solutions for fractional differential equations boundary value problems with Caputo derivative

作　　者：秦小娜[1] 贾梅[1] 刘帅[1] 

机构地区：[1]上海理工大学理学院,上海200093

出　　处：《山东大学学报（理学版）》2013年第10期62-67,77,共7页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助(11171220);上海市教委科研创新基金重点资助项目(10ZZ93)

摘　　要：研究了一类具有Caputo导数的分数阶微分方程边值问题正解的存在性,其中边界条件中含有分数阶导数,并且非线性项f:[0,1]×[0,+∞)→[0,+∞)满足Caratheodory条件。利用Krasnosel’skii锥上的不动点定理,得到了该边值问题至少存在一个正解和两个正解的充分条件。The paper is concerned with the existence of solutions for a class of fractional differential equations boundary value problems with Caputo derivative, where there exist fractional derivative in the boundary conditions and the nonlin- ear term f： ：[0,1]×[0,＋∞）→[0,＋∞）satisfies Caratheodory conditions. By using the Krasnosel＇ skii fixed theorem on a cone, the sufficient conditions for the problem at least one and two positive solutions are obtained.

关 键 词：正解 CAPUTO导数 边值问题 不动点定理 

分 类 号：O175.8[理学—数学]