四阶非线性微分方程组边值问题的正解  

Positive solutions of boundary value problems for systems of nonlinear fourth-order differential equations

作　　者：屈海东[1] 

机构地区：[1]韩山师范学院数学与信息技术系,广东潮州521041

出　　处：《云南大学学报（自然科学版）》2008年第S2期181-185,共5页Journal of Yunnan University(Natural Sciences Edition)

摘　　要：讨论了四阶非线性微分方程组-u(4)(x)=f(x,v),-v(4)(x)=g(x,u),u(0)=u′(0)=u″(0)=0,au″(1)+βu(1)=0,v(0)=v′(0)=v″(0)=0,av″(1)+βv(1)=0正解的存在性.在一定条件下,利用锥拉伸与锥压缩不动点定理获得了正解的存在性定理.The problem of existence of positive solutions for the next systems of nonlinear fourth-order differential equations was investigated: -u(4)(x)=f(x,v);-v(4)(x)=g(x,u);u(0)=u′(0)=u″(0)=0,au″(1)+βu(1)=0;v(0)=v′(0)=v″(0)=0,av″(1)+βv(1)=0.Under the suitable conditions,the existence and multiplicity of positive solutions were established by cone expansion and compression theorem in norm type.

关 键 词：边值问题 正解 格林函数 四阶 

分 类 号：O175.8[理学—数学]