Eigenvalue Criteria for Existence of Positive Solutions to Fractional Boundary Value Problem - Wen Lian; Zhanbing Bai (Journal of Function Spaces)
The existence and multiplicity of positive solutions for the nonlinear fractional differential equation boundary value problem (BVP) DC0+αyx+fx,yx=0,   0<x<1, y0=y′1=y″0=0 is established, where 2<α≤3,  CD0+α is the Caputo fractional derivative, and f:0,1×0,∞⟶0,∞ is a continuous function. The conclusion relies on the fixed-point index theory and the Leray-Schauder degree theory. The growth conditions of the nonlinearity with respect to the first eigenvalue of the related linear operator is given to guarantee the existence and multiplicity.