关于六阶边值问题解的存在性结果

SOME RESULTS ON THE SIXTH-ORDER BOUNDARY VALUE PROBLEMS

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.