非线性分数阶微分方程边值问题多重正解的存在性

The existence of multiple positive solutions for boundary value problem of nonlinear fractional differential equation

摘要: 研究了非线性分数阶微分方程边值问题 cDα0+u(t)+f(t,u(t))=0, 0cDα0+为Caputo分数阶导数.通过Green函数的性质,利用不动点定理得出了奇异和非奇异微分方程边值问题多重正解的存在性的一些理论以及奇异问题的唯一解存在性理论,并给出了相应的例证.

Abstract: We study the existence on multiple positive solutions for the nonlinear fractional differential equation boundary value problem cDα0+u(t)+f(t,u(t))=0, 0cDα0+ is the Caputo fractional derivative and 2α≤3 is a real number,f:×0,+∞) is continuous.By the properties of the Green function,fixed-point theorems,we give some multiple positive solutions for singular and nonsingular fractional differential equation boundary value problems,and we also give the uniqueness of solution for a singular problem.As applications examples are presented to illustrate the main results.