摘要：By constructing Green’s function, we give the natural formulae of solutions forthe following nonlinear impulsive fractional differential equation with generalizedperiodic boundary value conditions: { D t q c u ( t ) = f ( t , u ( t ) ) , t ∈ J ′ = J ∖ { t 1 , … , t m } , J = [ 0 , 1 ] , Δ u ( t k ) = I ( u ( t k ) ) , Δ u ′ ( t k ) = J k ( u ( t k ) ) , k = 1 , … , m , a u ( 0 ) − b u ( 1 ) = 0 , a u ′ ( 0 ) − b u ′ ( 1 ) = 0 , where 1 < q < 2 is a real number, D t q c is the standard Caputo differentiation. We present theproperties of Green’s function. Some sufficient conditions for the existence ofsingle or multiple positive solutions of the above nonlinear fractional differentialequation are established. Our analysis relies on a nonlinear alternative of theSchauder and Guo-Krasnosel’skii fixed point theorem on cones. As applications,some interesting examples are provided to illustrate the main results. MSC: 34B10, 34B15, 34B37.
关键词：impulsive fractional differential equation ; positive solutions ; boundary value problems ; fixed point theorem
