分数阶微分方程三点共振边值问题正解的存在性  

The Existence of Positive Solution for a Nonlinear Fractional Three-point Boundary Value Problem at Resonance

作　　者：王婷 达佳丽 WANG Ting;DA Jiali(Department of Mathematics,Zhixing College of Northwest Normal University,Lanzhou Gansu 730070,China)

机构地区：[1]西北师范大学知行学院数学系,甘肃兰州730070

出　　处：《西华师范大学学报（自然科学版）》2017年第4期415-419,429,共6页Journal of China West Normal University(Natural Sciences)

基　　金：甘肃省高等学校科研项目(2015B-203)

摘　　要：关于共振条件下分数阶微分方程边值问题的可解性的研究比较多,但在共振条件下正解的存在性的研究较少,本文运用了增算子的不动点理论,研究了分数阶微分方程三点边值问题在共振条件下正解的存在性,最后得到了一个正解存在的定理。Although there are many researches on the solvability of boundary value problems for fractional differential equations under the resonance conditions,the study on the existence of positive solutions is comparatively less.In this paper,the three point boundary value problem is studied by a new fixed point theorem of increasing operators and the existence of nonnegative solution is obtained.

关 键 词：分数阶微分方程 标准的Riemann Liouville微积分 共振 增算子的不动点定理 正解 

分 类 号：O193[理学—数学]