一类分数阶微分方程三点边值问题正解的存在性和多重性

Existence and multiplicity of positive solutions for a class of fractional differential equations of three-point boundary value problem

摘要: 利用积分方程技巧和锥上不动点指数理论,研究了一类非线性分数阶微分方程的三点边值问题,获得了该问题至少存在1个或2个正解的一系列充分条件.所得结果推广了整数阶微分方程的相应结果.最后,举例说明了所得结果的有效性.

Abstract: By applying the technique of integral equation and the fixed-point index theory in cone,this paper is concerned with three-point boundary value problems for nonlinear fractional differential equations.We obtain a series of sufficient conditions for the existence of at least one or two positive solution for this problem.These results extend the corresponding ones of ordinary differential equations of integer order.Finally,two examples are inserted to illustrate the effectiveness of the results.