Positive solutions for a class of fractional 3-point boundary value problems at resonance - Wang, Y.; Liu, Lishan (SpringerOpen, 2017)
In this paper, we study the nonlocal fractional differential equation: {Dα0+u(t)+f(t,u(t))=0,0<t<1,u(0)=0,u(1)=ηu(ξ), where 1<α<2, 0<ξ<1, ηξα−1=1, Dα0+ is the standard Riemann-Liouville derivative, f:[0,1]×[0,+∞)→R is continuous. The existence and uniqueness of positive solutions are obtained by means of the fixed point index theory and iterative technique.