| 摘要: |
| 利用Schauder不动点定理,研究二阶非线性微分方程u″=f(t,u,u'),t ≥ 1解(f∈C[[1,∞)×R×R,R])的渐近性,给出方程解渐近于直线at+b(a,b∈R)的一个充分条件.从而推广文献[2]定理1的结果,简化文献[3]中定理4成立的条件. |
| 关键词: 微分方程 渐近性 非线性 Schauder不动点定理 |
| DOI： |
| 投稿时间：2005-05-11修订日期：2005-06-17 |
| 基金项目: |
|
| Asymptotic Behaviour of the Solutions to a Class of Second Order Nonlinear Differential Equation |
|
Luo Zhimin, Luo Juan
|
| (Department. of Mathematics, Guangxi Normal University, Guilin, Guangxi, 541004, China) |
| Abstract: |
| This paper concerned about the asymptotic behavior of solutions of the nonlinear differential equation:u″=f(t,u,u'),t ≥ 1 where f∈C[[1,∞)×R×R,R].In our approach a key role is played by Schauder's fixed point theorem.A suffcient condition is given for this equation to have solutions behaving asymptotically like linear functions at+b where a,b∈R.Our results improve theorem 1 of Reference[2].And the conditions of theorem 4 of Reference[3] are simplified. |
| Key words: differential equation asymptotic behavior nonlinear Schauder's fixed point theorem |
