含参数及p-Laplacian算子的奇异分数阶微分方程积分边值问题的正解

Positive solutions for some singular fractional differential equation integral boundary value problems with p-Laplacian and a parameter

利用Green函数的性质构造出合适的锥,引入适当的高度函数并考虑高度函数在锥中某些有界集合上的积分,研究一类具有p-Laplacian算子的非线性奇异分数阶微分方程积分边值问题的局部正解以及多个局部正解。非线性项f允许关于时间和空间变量具有奇异性。

A special cone is constructed by means of the properties of Green function. By introducing height functions of the nonlinear term on some bounded sets and considering integrations of these height functions,several existence and multiplicity of local positive solutions theorems for some nonlinear fractional differential equation integral boundary value problems with p-Laplacian and a parameter are obtained. The nonlinear term f permits singularities with respect to both the time and space variables.