Existence of solutions for sub-linear or super-linear operator equations  

作　　者：CHEN YingYing DONG YuJun SHAN Yuan 

机构地区：[1]Department of Mathematics, Nanjing Normal University [2]Department of Mathematics, Nanjing University

出　　处：《Science China Mathematics》2015年第8期1653-1664,共12页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.11171157);the Jiangsu Planned Projects for Postdoctoral Research Funds

摘　　要：We investigate solutions to superlinear or sublinear operator equations and obtain some abstract existence results by minimax methods. These results apply to superlinear or sublinear Hamiltonian systems satisfying several boundary value conditions including Sturm-Liouville boundary value conditions and generalized periodic boundary value conditions, and yield some new theorems concerning existence of solutions or nontrivial solutions. In particular, some famous results about periodic solutions to superlinear or sublinear Hamiltonian systems by Rabinowitz or Benci and Rabinowitz are special cases of the theorems.We investigate solutions to superlinear or sublinear operator equations and obtain some abstract existence results by minimax methods. These results apply to superlinear or sublinear Hamiltonian systems satisfying several boundary value conditions including Sturm-Liouville boundary value conditions and generalized periodic boundary value conditions, and yield some new theorems concerning existence of solutions or nontrivial solutions. In particular, some famous results about periodic solutions to superlinear or sublinear Hamiltonian systems by Rabinowitz or Benci and Rabinowitz are special cases of the theorems.

关 键 词：SUPERLINEAR SUBLINEAR operator equations existence of solutions minimax methods Hamiltoniansystems 

分 类 号：O175[理学—数学]