%0 Journal Article
%T Existence and Multiplicity of Positive Solutions to a Class of Nonlinear Cantilever Beam Equations<br>一类非线性悬臂梁方程正解的存在性与多解性
%A YAO Qingliu
%A <br>姚庆六
%J 系统科学与数学
%D 2009
%I 
%X The positive solutions are studied for the nonlinear fourth-order ordinary differential equation $u^{(4)}(t)=f(t,u(t),u'(t)),~t\in 0,1]\backslash E$, subject tothe boundary conditions $u(0)=u'(0)=u'(1)=u''(1)=0$, where $E\subset 0,1]$ is a closed set with measure zero and nonlinear term $f(t,u,v)$ may be singular for $t\in E$. With some conditions, by constructing suitable integral equation and applying fixed point theorems on cone, the existence of $n$ positive solutions is proved for the equations, where $n$ is a positive integral number.
%K Nonlinear ordinary differential equation
%K boundary value problem
%K positive solution<br>非线性常微分方程
%K 边值问题
%K 正解
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=37F46C35E03B4B86&jid=0CD45CC5E994895A7F41A783D4235EC2&aid=207237BE8FDC2ACDA23651CF910A6C0C&yid=DE12191FBD62783C&vid=771469D9D58C34FF&iid=CA4FD0336C81A37A&sid=E84BBBDDD74F497C&eid=CB423C9A71560A74&journal_id=1000-0577&journal_name=系统科学与数学&referenced_num=3&reference_num=12