半正的分数阶微分方程(n-1,1)-型积分边值问题的多个正解

Multiple Positive Solutions for Semipositone(n-1,1)-Type Integral Boundary Value Problems of Nonlinear Fractional Differential Equations

采用Riemann-Liouville分数阶导数,研究了半正的分数阶微分方程(n-1,1)-型积分边值问题,获得了参数λ的一个区间,使得λ落在这个区间的时候,该半正的分数阶微分方程边值问题有多个正解.

In this paper,we consider the（n-1,1）-type integral boundary value problem of nonlinear fractional differential equation D0＋^α＋u（t）＋λf（t,u（t））=0,0t1 U^（（j））（0）=0≤j≤n-2 （） whereλ,μis a parameter and 0μa,a∈（n-1,n） is a real number and n≥3,D0＋^αis the Riemann-Liouville＇s fractional derivative,and / is continuous and semipositone.We derive an interval of A such that any A lying in this interval,the semipositone boundary value problem has multiple positive solutions.