一类非线性分数阶奇异微分方程正解的存在性

Positive Solutions for a Class of Singular Equation of Nonlinear Fractional Differential Equations

讨论了一类非线性分数阶奇异微分方程的存在性和唯一性,通过分数阶格林函数及其性质将微分方程转化为等价的积分方程,应用偏序上的不动点定理得到方程正解的存在性和唯一性.

In this work we discuss a boundary value problem for a singular equation of nonlinear fractional dif- ferential equations . The differential operator is taken in the standard Riemann-Liouville sense. By using Green function and its corresponding properties, we transform the derivative equation into equivalent integral equation. The existence and uniqueness of positive solution is based on a fixed theorem in partially ordered sets.