非共振半线性波方程系统周期解的存在性

Existence of Periodic Solution for System of Semilinear Wave Equations at Nonresonance

讨论半线性波方程系统utt- uxx=Au+g(t,x,u) +h(t,x)的周期 - Dirichlet边值问题 .借助 L yapunov- Schmidt方法 ,利用 L eray- Schauder不动点定理 ,在一定条件下证明了该系统存在一个解 .

The periodic Dirichlet boundary value problem is discussed for the system of semilinear wave equations u tt-u xx=Au+g(t,x,u)+h(t,x). By using Lyapunov Schmidt reduction method together with Leray Schauder fixed point theorem,the existence of solution for this system under suitable conditions is proved.