非线性二阶常微分方程Robin问题的正解  

Positive solutions of the Robin problem for nonlinear second-order ordinary differential equations

作　　者：杨志林[1] 

机构地区：[1]青岛理工大学理学院,青岛266033

出　　处：《青岛理工大学学报》2013年第1期5-14,43,共11页Journal of Qingdao University of Technology

摘　　要：研究如下非线性项带一阶导数的Robin问题:{u″+f(t,u,u′)=0,u(0)=u′(1)=0,其中f∈C([0,1]×R2+,R+)(R+=[0,+∞)).通过一个积分恒等式获得先验估计,在此基础上,用不动点指数理论建立上述边值问题正解的存在性,多重正解的存在性和正解的唯一性,并且用上下解方法证明了唯一正解可以通过迭代序列一致逼近得到.This paper deals with the Robin problem with the nonlinearity f depending on the first order derivative： {u＂＋f（t,u,u＇）=0 u（0）=u＇（1）=0, where f∈C（[0,1]×R2＋,R＋）（R＋=[0,＋∞））. Based on a prior1 estimated obtained by u- tilizing an integral identity , we use fixed point index theory to establish the existence, mul- tiplicity and uniqueness of positive solutions for the above problem. Furthermore, by using the method of super-and sub-solutions, we prove that the unique positive solution, if it turns to be this case, can be uniformly approximated by successive sequences.

关 键 词：ROBIN问题 正解 先验估计 积分恒等式 不动点指数 迭代序列 上下解 

分 类 号：O175.8[理学—数学] O177.91[理学—基础数学]