一类非线性四阶椭圆型方程边值问题解的存在唯一性  

The Existence and Uniqueness of Solutions to Some Nonlinear Fourth Order Elliptic Boundary Value Problems

作　　者：冯艳青[1] 王忠英[1] 

机构地区：[1]常州工学院数学系,江苏常州213002

出　　处：《数学年刊（A辑）》2014年第4期479-484,共6页Chinese Annals of Mathematics

基　　金：江苏省教育厅项目(No.13KJD110001);常州工学院自然科学基金(No.YN0909)的资助

摘　　要：借助路径提升问题,利用Banach空间吸引盆理论研究了四阶椭圆型方程边值问题解的存在唯一性,并给出了其解存在唯一的充分条件.文中主要结果为椭圆型方程解的理论研究提供了一类方法,也推广了Alexiades和Elcrat的有关工作.Using path-lifting problem and the basin of attraction method, the uniqueness and existence of the solution to some fourth order elliptic boundary value problems are studied. A set of sufficient conditions is given. The main results of this paper provide a method for studying the theory of the solution to the nonlinear elliptic equation, as well as generalize some existing results by Alexiades and Elcrat.

关 键 词：椭圆型方程 边值问题 吸引盆 路径提升问题 存在理论 

分 类 号：O177.2[理学—数学]