非共振下带非C^2扰动泛函的Duffing方程组两点边值问题的解(英文)

ON THE SOLUTION OF TWO-POINT BOUNDARY VALUE PROBLEM OF DUFFING SYSTEM WITH NON-C^2 PERTURBATION FUNCTIONAL AT NONRESONANCE

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]→R^n,g:[0,2π]×R^n→R^n是势Carathéodory向量值函数,e:[0,2π]→R^n是L^2[0,2π]中给定的向量值函数,a=(a_1,a_2,…,a_n)~T和b=(b_1,b_2,…,b_n)~T是两个给定的向量.利用L^2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.

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]→R^n,g:[0,2π]×R^n→R^n is a potential Carathéodory vector valued function,e:[0,2π]→R^n is a given vector valued function in L^2[0,2π], a=(a_l,a_2,…,a_n)~T and b=(b_l,b_2,…,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 L^2 space and an existence and uniqueness result on the above problem is presented.