【摘要】 本文讨论下列Duffing方程组两点边值问题的解{u″+g（t,u）=e（t）, u（0）=a,u（2π）=b,其中t∈[0,2π],u:[0,2π]→Rⁿ,g:[0,2π]×Rⁿ→Rⁿ是势Carathéodory向量值函数,e:[0,2π]→Rⁿ是L²[0,2π]中给定的向量值函数,a=（a₁,a₂,…,a_n）^T和b=（b₁,b₂,…,b_n）^T是两个给定的向量.利用L²空间中的一个minimax定理讨论了Duffing方程组边值问题的解,获得了这一边值问题的一个存在唯一性定理.更多还原

【Abstract】 This paper deals with the solution of the following two-point boundary value problem of Duffing system {u″+g（t,u）=e（t）, u（0）=a,u（2π）=b, where t∈[0,2π],u:[0,2π]→Rⁿ,g:[0,2π]×Rⁿ→Rⁿ is a potential Carathéodory vector valued function,e:[0,2π]→Rⁿ is a given vector valued function in L²[0,2π], a=（a_l,a₂,…,a_n）^T and b=（b_l,b₂,…,b_n）^T are two given vectors.The solution for the boundary value problem of Duffing system is investigated by using a minimax theorem in L² space and an existence and uniqueness result on the above problem is presented.更多还原