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

Existence of solutions for sub-linear or super-linear operator equations
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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.
出处 《Science China Mathematics》 SCIE CSCD 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
关键词 SUPERLINEAR SUBLINEAR operator equations existence of solutions minimax methods Hamiltoniansystems 超线性算子方程 解的存在性 Hamilton系统 亚线性 边值条件 哈密顿系统 极大极小 边界条件
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参考文献10

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