奇异分数微分方程耦合系统边值问题的正解(英文)  

Positive Solution to Boundary Value Problem for a Singular Coupled System of Fractional Differential Equations

作　　者：宋利梅[1] 

机构地区：[1]嘉应学院数学学院,广东梅州514015

出　　处：《安徽师范大学学报（自然科学版）》2011年第4期307-313,共7页Journal of Anhui Normal University(Natural Science)

基　　金：Supported by the Natural Science Foundation of Guangdong Province(10151063101000003)

摘　　要：研究一类Dirichlet型非线性α,β∈(3,4]阶奇异分数微分方程耦合系统边值问题,其中分数导数D0α+,D0β+是标准的Riemann-Liouville分数导数.利用锥上Krasnosel’skii不动点定理和Leray-Schauder非线性二择一定理,得到该边值问题正解存在的若干准则.文中还举例说明了所得结果的可应用性.In this paper,we study a Dirichlet-type boundary value problem（BVP） of nonlinear fractional differential equation with an order α,β∈（3,4],where the fractional derivative Dα0＋,Dβ0＋ is the standard Riemann-Liouville fractinal derivative.By means of the Leray-Schauder nonlinear alternative and Krasnosel＇skii fixed-point theorem in cones,we obtain some criteria for the existence of one positive solution for the above BVP.We also give examples to illustrate the applicability of our results.

关 键 词：奇异耦合系统 分数微分方程 边值问题 正解 锥上不动点定理 

分 类 号：O175[理学—数学]