Existence of Positive Solutions for Fractional Differential Equation with Nonlocal Boundary Condition - Hongliang Gao; Xiaoling Han (International Journal of Differential Equations)
By using the fixed point theorem, existence of positive solutions for fractional differential equation with nonlocal boundary condition D0+αu(t)+a(t)f(t,u(t))=0, 0<t<1, u(0)=0, u(1)=∑i=1∞αiu(ξi) is considered, where 1<α≤2 is a real number, D0+α is the standard Riemann-Liouville differentiation, and ξi∈(0,1),  αi∈[0,∞) with ∑i=1∞αiξiα-1<1, a(t)∈C([0,1],[0,∞)),  f(t,u)∈C([0,1]×[0,∞),[0,∞)).