一类奇异非局部分数微分方程特征值问题的正解

Existence of Positive Solutions for a Singular Nonlocal Fractional Differential Equation Eigenvalue Problem

通过引进一个简单的积分条件,在非线性项f允许在t=0,1和u=0处奇异的情况下,研究一类奇异非局部分数阶微分方程特征值问题,首先给出Green函数及其性质,然后应用Schauder不动点定理和上下解方法建立了正解存在的新结果,而且一些特殊情况也被讨论,深远的结果被得到.最后也给出一个例子说明主要结果的应用.

By introducing a simple integral condition, in the case where nonlinearity is allowed to have singularity at t = O, 1 and u = O, a class of the eigenvalue problem of singular nonlocal fractional differential equation is studied. We firstly give the Green function and its properties, and then establish the new results of existence for positive solution by using the Schauder＇ s fixed point theorem and upper and lower solution method. Some special cases are discussed and specialc ase discussed and some further results obtained. Also, an example is given to illustrate the application of main results.