摘要
讨论了以下三阶非线性微分方程组{-u′′′(x)=f(x,v),-v′′′(x)=g(x,u),x (0,1),u(0)=0,αu′(0)-βu″(0)=0,γu′(1)+δu″(1)=0,v(0)=0,αv′(0)-βv″(0)=0,γv′(1)+δv″(1)=0.在假设条件下,利用锥拉伸与锥压缩不动点定理获得了上述方程组正解的存在性.
The folllowing boundary value problem of the nonlinear third - order differential system is investigated： {=μ′″（x）=f（x,v）, =v′″（x）=g（x,μ）,x∈（0,1）, μ（0）=0,αμ′（0）-βμ″（0）=0,γμ′（1）＋δμ″（1）=0, v（0）=0,αv′（0）-βv″（0）=0,γv′（1）＋δv″（1）=0.Under some suitable conditions, the existence and multiplicity of positive solutions are established by cone expansion and compression theorems in norm type.
出处
《华南师范大学学报（自然科学版）》
CAS
北大核心
2009年第2期16-19,共4页
Journal of South China Normal University(Natural Science Edition)
关键词
边值问题
正解
格林函数
三阶非线性微分方程组
boundary value problem
positive solution
Green＇s function
nonlinear third order differential system
