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

被引：10

作者：

Chen YingYing ^{[1
]}

Dong YuJun ^{[1
]}

Shan Yuan ^{[2
]}

机构：

[1] Nanjing Normal Univ, Dept Math, Nanjing 210097, Jiangsu, Peoples R China

[2] Nanjing Univ, Dept Math, Nanjing 210093, Jiangsu, Peoples R China

来源：

SCIENCE CHINA-MATHEMATICS | 2015年 / 58卷 / 08期

基金：

中国国家自然科学基金;

关键词：

superlinear; sublinear; operator equations; existence of solutions; minimax methods; Hamiltonian systems;

D O I：

10.1007/s11425-014-4966-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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-Rabinowitz are special cases of the theorems.

引用

页码：1653 / 1664

页数：12

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