【摘要】 利用最小作用原理研究2阶系统ü(t)-A(t)u(t)=▽F(t,u(t)),u(0)-u(T)=u.(0)-u.(T)=0{,a.e.t∈[0,T]的周期解的存在性,在非线性项是次线性及A(t)是1个连续N阶对称矩阵的条件下得到了该系统的2个新的存在性定理.更多还原

【Abstract】 The existence of periodic solutions of the following second order systems ü(t)-A(t)u(t)=▽F(t,u(t)),u(0)-u(T)=u·(0)-u·(T)=0,a.e.t∈ is studied by the least action principle.When the nonlinearity is sublinear and A(t) is a continuous symmetric matrix of N order,two new existence theorems of this system are obtained.更多还原