稳态吊桥方程耦合系统正解的存在性

本文研究了二阶和四阶常微分方程耦合系统u~((4))(t)=λf(t,v(t)),t∈(0,1),-v″(t)=λg(t,u(t)),t∈(0,1),u(0)=u(1)=u″(0)=u″(1),v(0)=v(1)正解的存在性,其中λ0为参数,f,g∈C(0,1]×0,∞),R).当f,g满足适当的条件时,本文证明了λ充分大时方程一个正解的存在性.主要结果的证明基于Schauder不动点定理.

An existence result on positive solutions for a coupled system of steady state suspension bridge equations

In this paper, we are concerned with the existence of positive solutions of a coupled system of second-order and fourth-order ordinary differential equations \ \begin{cases} &~u''(t)=\lambda f(t,v(t)), \ \ \ \ \ \ t\in (0,1),\&-v''(t)=\lambda g(t,u(t)), \ \ \ \ \ t\in (0,1),\&~u(0)=u(1)=u''(0)=u''(1)=0,\&~v(0)=v(1)=0,\\end{cases} \] where $\lambda$ is a positive parameter, $f,~g\in C(0,1]\times0,\infty),~\mathbb{R})$. We prove the existence of a large positive solution for $\lambda$ large under suitable assumptions on $f$ and $g$. The proof of our main result is based upon the Schauder''s fixed point theorem.