Infinitely many rotating periodic solutions for local superquadratic damped Hamiltonian systems with sublinear impulsive effects

Abstract

In this paper, we consider the following damped second-order Hamiltonian systems with impulsive effects{−u¨(t)−g(t)u˙(t)+B(t)u(t)=∇uF(t,u(t)),a.e. t∈R,Δ(u˙i(tj))=Iij(ui(tj)),i=1,2,⋯,n,j=1,2,⋯,m,u(T)=Qu(0),u˙(T)=Qu˙(0), where T>0, g∈L1([0,T],R), g(t+T)=g(t) with ∫0Tg(s)ds=0, Q∈O(n), B∈C(R,Rn×n) is symmetric with B(t+T)Q=QB(t), F∈C1(R×Rn,R) is local superquadratic, and every impulsive term Iij∈C(R,R)(i=1,2,⋯,n, j=1,2,⋯,m) is sublinear at the infinity and vector field (I1j(u1),I2j(u2),…,Inj(un))T(j=1,2,⋯,m) is unnecessary to be equipotential field. A sequence of nontrivial rotating periodic weak solutions is obtained via the Symmetric Mountain Pass Lemma due to Chang, which generalizes several previous results.