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.
出处
《青岛理工大学学报》
CAS
2013年第1期5-14,43,共11页
Journal of Qingdao University of Technology
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
Robin problem
positive solution
a priori estimate
integral identity
fixed pointindex
iterative sequence
super-and sub-solution
