分数阶周期边值问题的上下解方法

Upper and Lower Solution Method of Fractional-Order Periodic Boundary Value Problem

应用上下解方法,研究分数阶周期边值问题x(δ)(t)=f(t,x(t)),t∈[a,a+T],a>0,x(a)=x(a+T)解的存在性,其中:f是连续函数,f(a+T,x)=f(a,x),a>0,T>0是常数;δ∈(0,1].

Using upper and lower solution method, we studied the existence of solution of fractionalorder periodic boundary value problem x（δ）（t）=f（t,x（t））,t∈[a,a＋T],a〉0,x（a）=x（a＋T） where f is a continuous function, f（a＋T,x）=f（a,x）,a〉0,T〉0 are constants and ;δ∈（0,1].