摘要
本文得到了四阶方程边值问题u(4)=f(u(x)),u(0)=u(0)=u(0)=0,ku(1)=u(1)相应的Green函数G(x,t)。从而将该问题转化为Hammerstein型积分方程,并利用锥拉伸与锥压缩不动点定理,讨论了其正解的存在性与多重性,得到了相应的结论。
In this paper, we obtain the Green function of the fourth order boundary value problem u^(4)=f(u(x)), u′(0)=u″(0)= u′″(0)=0, ku(1) = u′″(1). This problem is turned to a class of Hammerstein integral equations. The existence and multiplicity of positive solutions for this problem are proved by using a Fixed Point Theorem in cone.
出处
《工程数学学报》
CSCD
北大核心
2005年第5期864-868,共5页
Chinese Journal of Engineering Mathematics
基金
北京市教委科研基金
山西省自然科学基金.
关键词
四阶方程
边值问题
正解
fourth order equation
boundary value problem
positive solution