高阶非线性分数阶微分方程解的存在性和唯一性

Higher order nonlinear fractional differential equation existence and uniqueness of solutions

研究了一类高阶非线性分数阶三点边值问题非平凡解的存在性和唯一性,主要是通过有序的实Banach空间上的非线性算子方程x=A(x,x)+B(x,x)+e来研究的.其中A,B为混合单调算子,利用锥上的不动点定理,得到了非平凡解的存在性和唯一性,又构造了两个迭代序列来近似的逼近解.此外,作为主要的结果应用,给出了一个例子来说明.

The existence and uniqueness of nontrivial solutions for a class of higher-order nonlinear fractional order three-point boundary value problems are studied,mainly through nonlinear operator equations x=A(x,x)+B(x,x)+e in ordered real Banach spaces,A,B are mixed monotone operators.Using the fixed point theorem on cones,the existence and uniqueness of nontrivial solutions are obtained,and two iterative sequences are constructed to approximate the approximate solutions.In addition,as our main result application,an example is given to illustrate.