一类Capillarity系统非平凡解的存在性研究

发布时间：2018-05-15 13:41

  本文选题：乘积空间 + m增生映射　； 参考：《数学杂志》2017年02期

【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+1p_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.
[Abstract]:In this paper, we study the existence of solutions for a class of capillarity systems. By using the method of defining nonlinear mapping in the product space, the capillarity system is transformed into a nonlinear operator equation. By means of Sobolev embedding theorem, the compactness of nonlinear maps is proved, and the existence of solutions of nonlinear operator equations is obtained by using the properties of the range of nonlinear mappings. Under certain conditions, it is obtained that the capillarity system can be used in LP1 (惟) 脳 L ~ (2 +) P ~ (2 +) (惟) 脳. A conclusion on the existence of nontrivial solutions in a 脳 L ~ (1) PMN (惟) space, where 惟 is a bounded conical domain in R~N(N 鈮，

本文编号：1892701