一类具有无穷点积分边界条件非线性分数阶微分方程解的存在性与多解性

Existence and Multiplicity of Solutions for a Class of Nonlinear Fractional Differential Equations with Infinite-Point Integral Boundary Conditions

考虑一类带有无穷点积分边界条件的非线性分数阶微分方程,通过计算Green函数,将微分方程转化为积分方程,并在分析Green函数性质的基础上,应用不动点指数定理得到了该边值问题解的存在性和多解性.

We considered a class of nonlinear fractional differential equations with infinite-point integral boundary conditions. By calculating the Green＇s function, we transformed the differential equation into integral equation. On the basis of analysis of the properties of Green＇s function, we used the indexed fixed point theorem to obtain the existence and multiplicity of solutions of the boundary value problem.