There are many works on the asymptotic stability of second dimensional nonlinear differential equation. In particular, these results only concern with the system which includes one or two terms, whereas few works conc...There are many works on the asymptotic stability of second dimensional nonlinear differential equation. In particular, these results only concern with the system which includes one or two terms, whereas few works concern with system which includes more than two terms. In this paper, system which includes four nonlinear terms are studies. We obtain the global asymptotic stability of zero solution, and discard the condition which require the Liapunov function trends to infinity, and only require that the positive orbit is bounded.展开更多
This paper deals with the existence and nonexistence of global positive solution of the following equation:where p, q, m, α are parameters with is a bounded domain with Ω smooth enough, The necessary and sufficient ...This paper deals with the existence and nonexistence of global positive solution of the following equation:where p, q, m, α are parameters with is a bounded domain with Ω smooth enough, The necessary and sufficient conditions for the global existence of solution are obtained.展开更多
The author considers the Klien-Gordon equations utt --△u+μu= f(u) (P >0, |f(u)| ≤ c|u|α+1 ). The necessary and sufficient condition of existence of global solutions is obtained for f(s)dsdx <d (d is the give...The author considers the Klien-Gordon equations utt --△u+μu= f(u) (P >0, |f(u)| ≤ c|u|α+1 ). The necessary and sufficient condition of existence of global solutions is obtained for f(s)dsdx <d (d is the given constant).展开更多
The authors study a resonant Klein-Gordon system with convenient nonlinearities in two space dimensions, prove that such a system has global solutions for small, smooth,compactly supported Cauchy data, and find that t...The authors study a resonant Klein-Gordon system with convenient nonlinearities in two space dimensions, prove that such a system has global solutions for small, smooth,compactly supported Cauchy data, and find that the asymptotic profile of the solution is quite different from that of the free solution.展开更多
文摘There are many works on the asymptotic stability of second dimensional nonlinear differential equation. In particular, these results only concern with the system which includes one or two terms, whereas few works concern with system which includes more than two terms. In this paper, system which includes four nonlinear terms are studies. We obtain the global asymptotic stability of zero solution, and discard the condition which require the Liapunov function trends to infinity, and only require that the positive orbit is bounded.
文摘This paper deals with the existence and nonexistence of global positive solution of the following equation:where p, q, m, α are parameters with is a bounded domain with Ω smooth enough, The necessary and sufficient conditions for the global existence of solution are obtained.
文摘The author considers the Klien-Gordon equations utt --△u+μu= f(u) (P >0, |f(u)| ≤ c|u|α+1 ). The necessary and sufficient condition of existence of global solutions is obtained for f(s)dsdx <d (d is the given constant).
基金Project supported by the National Natural Science Foundation of China (No.10271108).
文摘The authors study a resonant Klein-Gordon system with convenient nonlinearities in two space dimensions, prove that such a system has global solutions for small, smooth,compactly supported Cauchy data, and find that the asymptotic profile of the solution is quite different from that of the free solution.
