Some Abstract Critical Point Theorems for Self-adjoint Operator Equations and Applications  

作　　者：Chungen LIU Qi WANG 

机构地区：[1]School of Mathematics and LPMC, Nankai University, Tianjin 300071, China [2]School of Mathematics, Nankai University, Tianjin 300071, China

出　　处：《Chinese Annals of Mathematics,Series B》2011年第1期1-14,共14页数学年刊（B辑英文版）

基　　金：Project supported by the National Natural Science Foundation of China (Nos.11071127,10621101,10901118);the 973 project of the Ministry of Science and Technology of China (No.2011CB808002)

摘　　要：By using the index theory for linear bounded self-adjoint operators in a Hilbert space related to a fixed self-adjoint operator A with compact resolvent,the authors discuss the existence and multiplicity of solutions for(nonlinear) operator equations,and give some applications to some boundary value problems of first order Hamiltonian systems and second order Hamiltonian systems.

关 键 词：Self-adjoint operator equations Index theory Relative Morse index Dual variational method Morse theory Hamiltonian systems 

分 类 号：O177.6[理学—数学] TP317[理学—基础数学]