一类分数阶微分方程边值问题正解的存在性

The existence of positive solutions to boundary value problems for a class of fractional differential equations

对于非线性分数阶微分方程{D0^+^α+u(t)-λu(t)=λf(t/t^1-αu(t))0<t≤1,limt→0^+t^1-αu(t)=u(1),其中:0<α≤1;λ<0;μ>0;f∈C((0,1]×[0,+∞),[0,+∞));D0^+αu为标准的Riemann-Liouville分数阶导数,运用上下解方法和单调迭代方法研究了边值问题正解的存在性.

For fractional differential equations{D0^+^α+u(t)-λu(t)=λf(t/t^1-αu(t))0<t≤1,limt→0^+t^1-αu(t)=u(1),where 0<α≤1;λ<0;μ>0;f∈C((0,1]×[0,+∞),[0,+∞)),D0^+α u is standard Riemann-Liouville fractional derivative,considers the existence of positive solutions to boundary value problems by using1 of upper and lower solution method and monotone iterative method.