P-symmetric Subharmonic Solutions for Nonlinear Hamiltonian Systems

作     者：Duan Zhi ZHANG Zhi Hao ZHAO Duan Zhi ZHANG;Zhi Hao ZHAO

作者机构：School of Mathematical SciencesNankai UniversityTianjin 300071P.R.China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2024年第40卷第6期

页      面：1388-1408页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：partially supported by National Key R&D Program of China(Grant No.2020YFA0713300) NSFC Grants(Grant Nos.17190271 and 11171341) LPMC of Nankai University partially supported by the NSFC Grants(Grant Nos.12171253 and 17190271) LPMC of Nankai University 

主　　题：P-symmetric subharmonic Hamiltonian systems Maslov-type index theory iteration inequality asymptotically linear 

摘      要：In this paper,we prove that for each positive k≡1 mod m there exists a P-symmetric kmτ-periodic solution xk for asymptotically linear mτ-periodic Hamiltonian systems,which are nonautonomous and endowed with a *** the P-symmetric Hamiltonian function is semi-positive,one can prove,under a new iteration inequality of the Maslov-type P-index,that xk_(1) and xk_(2) are geometrically distinct for k_(1)/k_(2)≥(2n+1)m+1;and xk_(1),xk_(2) are geometrically distinct for k_(1)/k_(2)≥m+1 provided xk_(1) is non-degenerate.