P-symmetric Subharmonic Solutions for Nonlinear Hamiltonian Systems  

作　　者：Duan Zhi ZHANG Zhi Hao ZHAO 

机构地区：[1]School of Mathematical Sciences,Nankai University,Tianjin 300071,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2024年第6期1388-1408,共21页数学学报（英文版）

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。

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 P-symmetry.If 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.

关 键 词：P-symmetric subharmonic Hamiltonian systems Maslov-type index theory iteration inequality asymptotically linear 

分 类 号：O175[理学—数学]