MULTIPLE SOLUTIONS FOR A HAMILTONIAN ELLIPTIC SYSTEM WITH SIGN-CHANGING PERTURBATION  

作　　者：Peng CHEN Longjiang GU Yan WU 陈鹏;谷龙江;吴艳

机构地区：[1]Three Gorges Mathematical Research Center,China Three Gorges University,Yichang 443002,China [2]College of Science,China Three Gorges University,Yichang 443002,China [3]School of Mathematics and Physics,China University of Geosciences,Wuhan 430074,China [4]School of Mathematics and Statistics,Wuhan University of Technology,Wuhan 430070,China

出　　处：《Acta Mathematica Scientia》2025年第2期602-614,共13页数学物理学报(B辑英文版)

基　　金：supported by the NSFC(11301297);the Hubei Provincial Natural Science Foundation of China(2024AFB730);the Yichang City Natural Science Foundation(A-24-3-008);the Open Research Fund of Key Laboratory of Nonlinear Analysis and Applications(Central China Normal University),Ministry of Education,P.R.China(NAA2024ORG003);Gu's research was supported by the Zhejiang Provincial Natural Science Foundation(LQ21A010014);the NFSC(12101577).

摘　　要：In this paper,we study the elliptic system{-Δu+V(x)u=|v|^(p-2)v-λ_(2)|v|^(s2-2)v,-Δu+V(x)v=|u|^(p-2)u-λ_(1)|u|^(s1-2)u,u,v∈H^(1)(R^(N))with strongly indefinite structure and sign-changing nonlinearity.We overcome the absence of the upper semi-continuity assumption which is crucial in traditional variational methods for strongly indefinite problems.By some new tools and techniques we proved the existence of infinitely many geometrically distinct solutions if parametersλ_(1),λ_(2)>0 small enough.To the best of our knowledge,our result seems to be the first result about infinitely many solutions for Hamiltonian system involving sign-changing nonlinearity.

关 键 词：variational method strongly indefinite elliptic system multiple solutions signchanging nonlinearity 

分 类 号：O175.25[理学—数学]