研究非线性Klein-Gordon方程的柯西问题u_(tt)-Δu+u=u|u|~(p-1),x∈R~n,t>0;u(x,0)=u_0(x),u_t(x,0)=u_1(x),x∈R~n.通过引进一族位势井,得到了解的整体存在性与不存在的门槛结果.

We study the Cauchy problem of nonlinear Klein-Gordon equation u_(tt)-Δu+u=u|u|~(p-1),x∈R~n,t>0; u(x,0)=u_0(x),u_t(x,0)=u_1(x),x∈R~n. By introducing a family of potential wells we obtain a threshold result of global existence and nonexistcnce of solutions.