一类高阶分数阶非线性微分方程组多点边值问题正解的存在性

Existence of Positive Solutions to Multi-point Boundary Value Problem for Nonlinear High-order Fractional Differential Equations

运用不动点指数理论,讨论了一类高阶分数阶非线性微分方程组多点边值问题,研究了该问题正解的存在性、多重性以及不存在准则,给出了保证正解存在的一些极限型条件,条件适用于更一般的非线性项.

A multi-point boundary value problem of nonlinear high-order fractional differential equations is studied,applying fixed-point index theory,the existence,multiplicity and non-existence criteria of positive solutions to this problem are studied,and some limit type conditions guaranteeing the existence of positive solutions are given,which can be applied to more general nonlinearities.