一类分数阶微分方程周期边值问题正解的存在性  

Existence of Positive Solutions to Periodic Boundary Value Problems for a Class of Fractional Differential Equations

作　　者：吕莉 李小龙 LV Li;LI Xiao-long(School of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)

机构地区：[1]西北师范大学数学与统计学院

出　　处：《兰州文理学院学报（自然科学版）》2019年第6期12-15,18,共5页Journal of Lanzhou University of Arts and Science(Natural Sciences)

基　　金：甘肃省自然科学基金(18JR3RA084)

摘　　要：运用Krasnosel’skii不动点定理研究了分数阶微分方程周期边值问题{D0^α+u(t)-λu(t)=μf(t,t^1-αu(t)),0<t≤1,limt→0+t^1-αu(t)=u(1),0<α≤1正解的存在性.其中λ<0,μ>0,Dα0+u是u(t)的Riemann-Liouville分数阶微分,f∶(0,1]×[0,+∞)→[0,+∞)为连续函数.This paper studies the existence of nonnegative solutions to periodic boundary value problems of fractional differential equations by means of Krasnosel’skii fixed-point theorem,{D0^α+u(t)-λu(t)=μf(t,t^1-αu(t)),0<t≤1,lim t→0+t^1-αu(t)=u(1),0<α≤1 Where λ<0,μ>0,Dα0+u is the Riemann-Liouville fractional derivative of u(t),f∶(0,1]×[0,+∞)→[0,+∞)is a continuous function.

关 键 词：分数阶微分方程 周期边值问题 Krasnosel’skii不动点定理 GREEN函数 

分 类 号：O175.8[理学—数学]