一类Capillarity系统非平凡解的存在性研究  

STUDY ON THE EXISTENCE OF NON-TRIVIAL SOLUTION OF ONE KIND CAPILLARITY SYSTEMS

作　　者：魏利[1] 陈蕊 WEI Li CHEN Rui(School of Mathematics and Statistics, Hebei University of Economics and Business Shijiazhuang 050061, China)

机构地区：[1]河北经贸大学数学与统计学学院,河北石家庄050061

出　　处：《数学杂志》2017年第2期390-400,共11页Journal of Mathematics

基　　金：国家自然科学基金资助(11071053);河北省自然科学基金项目资助(A2014207010);河北省教育厅科学研究重点项目资助(ZH2012080);河北经贸大学科学研究重点项目资助(2015KYZ03)

摘　　要：本文研究了一类capillarity系统解的存在性问题.采用在乘积空间中定义非线性映射的方法,把capillarity系统转化为非线性算子方程.借助于Sobolev嵌入定理等技巧证明非线性映射具有紧性,进而利用非线性映射值域的性质得到非线性算子方程解的存在性的结论.并由此获得在一定条件下capillarity系统在L^(P1)(Ω)×L^(P2)(Ω)×…×L^(PM)(Ω)空间中存在非平凡解的结论,其中Ω为R^N(N≥1)中有界锥形区域且2N/N+1<p_i<+∞,i=1,2,…,M.本文所研究的问题和所采用的方法推广和补充了以往的相关研究工作.In this paper,the existence of solution of one kind capillarity systems was studied.The capillarity systems are converted to nonlinear operator equation in view of the method of defining nonlinear mappings in product space.By using the techniques of Sobolev embedding theorems etc.,the compactness of the nonlinear mapping is proved.Some properties of nonlinear mappings are employed to obtain the result that the nonlinear operator equation has solutions.Finally,the result that capillarity systems have non-trivial solution in L（P1）（Ω）×L（P2）（Ω）×…×L（PM）（Ω）is proved,where Ω is the bounded conical domain of RN（N≥1） and 2N/N＋1〈pi〈＋∞,for i = 1,2,…,M.The system studied and the methods used in this paper extend and complement some previous corresponding work.

关 键 词：乘积空间 m增生映射 CARATHEODORY条件 嵌入 紧映射 capillarity系统 

分 类 号：O177.91[理学—数学]