一类Caputo型分数阶微分方程边值问题多重正解存在的充分条件

Sufficient conditions for the existence of multiple positive solutions for a Caputo type fractional-order differential equation boundary value problems

研究了一类非线性项带有分数阶导数的Caputo型分数阶微分方程的边值问题.首先,将方程转化为等价的积分方程;其次,通过计算得到了与该方程相应的格林函数,并且分析了所得的格林函数的性质;最后,利用格林函数的性质以及Guo-Krasnosel’skii不动点定理和Leggett-Williams不动点定理得到了该边值问题分别存在1个正解和3个正解的充分条件.

The boundary value problems of Caputo type fractional differential equations with nonlinear terms and fractional derivatives were studied.Firstly,the equation was transformed into an equivalent integral equation.Secondly,Green function corresponding to the equation was obtained through calculation,and the properties of the obtained Green function were analyzed.Finally,by using the properties of Green function and the Guo-Krasnoselskii fixed point theorem and Leggett-Williams fixed point theorem,the sufficient conditions for the existence of one positive solution and three positive solutions for the boundary value problems were obtained.