Positive solutions for fractional differential equations with three-point multi-term fractional integral boundary conditions

摘要

We are concerned with the existence of at least one, two or three positive solutions for the boundary value problem with three-point multi-term fractional integral boundary conditions: { D q u ( t ) + f ( t , u ( t ) ) = 0 , 1 < q ≤ 2 , 0 < t < 1 , u ( 0 ) = 0 , u ( 1 ) = ∑ i = 1 m α i ( I p i u ) ( η ) , 0 < η < 1 , where D q is the standard Riemann-Liouville fractional derivative. Our analysis relies on the Krasnoselskii fixed point theorem and the Leggett-Williams fixed point theorem. Some examples are also given to illustrate the main results. MSC:26A33, 34A08, 34B18.