关于六阶边值问题解的存在性结果  

SOME RESULTS ON THE SIXTH-ORDER BOUNDARY VALUE PROBLEMS

作　　者：吴莉 张丽媛 Wu Li;Zhang Liyuan(Department of Mathematics and Physics,Nanjing Institute of Technology,Nanjing 211167;Department of mathematics,Nanjing university of Aeronautics and Astronautics,Nanjing 211106;Xingtai No.2 Middle School,Xingtai 054001)

机构地区：[1]南京工程学院数理部,南京211167 [2]南京航空航天大学理学院,南京211106 [3]邢台第二中学,邢台054001

出　　处：《南京大学学报（数学半年刊）》2021年第1期114-128,共15页Journal of Nanjing University(Mathematical Biquarterly)

摘　　要：本文主要建立非线性六阶周期边值问题{u^((6))+αu^((4))-βu"+γu=f(x,u),0≤x≤1,u^((i))(0)=u^((i))(1)=0,i=0,2,4正解的存在性结果,其中α,β,γ∈R和fi:[0,1]×[0,∞]→[0,∞]是连续函数.主要结论的证明基于不动点指数定理.In this paper,we establish some existence results of positive solutions of the nonlinear sixth-order periodic boundary value problem:{u^((6))+αu^((4))-βu"+γu=f(x,u),0≤x≤1,u^((i))(0)=u^((i))(1)=0,i=0,2,4whereα,β,γ∈R,f:[0,1]×[0,∞]→[0,∞]is continuous.The proof is based on the fixed point index theorem.

关 键 词：六阶微分方程 正解 锥 不动点指数定理 

分 类 号：O175.8[理学—数学]