【摘要】 二阶系统广泛存在于数理科学、生命科学以及社会科学的整个领域,特别是天体力学、航天科学以及生物工程中的很多模型都以二阶系统形式出现.研究以下二阶系统u¨(t)+q(t)u·(t)-A(t)u(t)+F(t,u(t))=0,a.e.t∈[0,T],u(0)-u(T)=u·(0)-eG(T)u·(T)={0的周期解的存在性.含有阻尼项q(t)u·(t)的二阶系统在物理上称为共振问题,因此对该系统的研究具有重要的物理意义.在F(t,x)满足某些新的存在性条件下,通过使用临界点理论中的鞍点定理获得了一个新的存在性定理.更多还原

【Abstract】 The second order system is widely used in the mathematical sciences,life sciences,as well as the whole field of social sciences,especially many models in celestial mechanics,space science and bio-engineering present in the form of the second order system.The purpose of this paper is to study the existence of periodic solutions of the following second order system u¨(t) + q(t).u(t)-A(t) u(t) + F(t,u(t)) = 0,a.e.t ∈[0,T],u(0)-u(T) =.u(0)-eG(T).u(T) = 0 {.The second order system with damping term in physics is called the vibration problem,it has important physical meaning to research this system.When F(t,x) satisfies some new existence conditions,one new existence theorem is obtained by the saddle point theorem.更多还原