稳态吊桥方程耦合系统正解的存在性  

Existence of positive solutions for a coupled system of steady state suspension bridge equation

作　　者：李涛涛[1] 

机构地区：[1]西北师范大学数学与统计学院,兰州730070

出　　处：《四川大学学报（自然科学版）》2017年第3期473-476,共4页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(11671322);国家自然科学基金天元基金(11626016)

摘　　要：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λ>0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.In this paper, we are concerned with the existence of positive solutions of a coupled system of second-order and fourth-order ordinary differential equation where λ is a positive parameter, f,g∈C（[0,1]×[0,∞）,R）. We obain the existence of a large positive solution under suitable assumptions on f and g. The proof is based upon the Schauder＇s fixed point theorem.

关 键 词：微分方程系统 正解 存在性 SCHAUDER不动点定理 

分 类 号：O175.8[理学—数学]