带p-Laplacian算子的分数阶微分方程半正系统正解的存在性

Existence of positive solutions for semipositone systemof fractional differential equations with p -Laplacian operator

对一类带有p-Laplacian算子和含有分数阶积分的奇异非线性项的Riemann-Liouville型分数阶微分方程半正系统正解的存在性进行了分析与研究,其边界条件包括不同阶的分数阶导数、Riemann-Stieltjes积分和无穷点边值条件.基于相关Green函数的性质以及不动点指数定理,得到了参数属于合适区间时,该系统至少存在一个正解的充分条件.通过具体实例验证了所得结果的实用性.

The existence of positive solutions for a semipositone system of Riemann-Liouville fractional differential equations with p-Laplacian operator and singular nonlinearities including fractional integral,subject to boundary conditions which contain fractional derivatives of differential order,Riemann-Stieltjes integrals and infinite point boundary condition is analyzed.Based on the properties of the related Green function and the fixed point index theorem,a sufficient condition for the existence of at least one positive solution of the system is obtained when the parameters belong to a suitable interval.The practicability of the results was verified by a substantial example.