| 一类三阶周期边值共振问题解的存在性 |
| |
| 引用本文： | 魏丽萍.一类三阶周期边值共振问题解的存在性[J].四川大学学报(自然科学版),2018,55(2):260-264. |
| |
| 作者姓名： | 魏丽萍 |
| |
| 作者单位： | 西北师范大学 |
| |
| 基金项目： | 国家自然科学基金资助项目(11671322);天元基金(11626061) |
| |
| 摘 要： | 本文研究了三阶周期边值共振问题{v'(t)=f(t,v(t)),t∈0,T],v~(i)(0)-v~(i)(T)=0,i=0,1,2解的存在性,其中函数f:0,T]×R→R连续且有界.当非线性项f满足适当条件时,本文发展了上下解方法并得到其解的存在性.主要结果的证明基于Lyapunov-Schmidt过程和解集连通理论.
|
| 关 键 词： | Lyapunov-Schmidt~过程 ~连通集 ~无序上下解 ~共振 ~存在性 |
| 收稿时间： | 2017/5/26 0:00:00 |
| 修稿时间： | 2017/9/8 0:00:00 |
Existence of Solutions for a Class of Third-Order Periodic Boundary Value Problems at Resonance |
| |
| WEI Li-Ping.Existence of Solutions for a Class of Third-Order Periodic Boundary Value Problems at Resonance[J].Journal of Sichuan University (Natural Science Edition),2018,55(2):260-264. |
| |
| Authors: | WEI Li-Ping |
| |
| Institution: | Northwest Normal University |
| |
| Abstract: | By using the Lyapunov-Schmidt procedure and the connectivity theory of the solution set of compact vector fields,~we develope the method of upper and lower solutions and obtain the existence of solutions for a third-order periodic boundary value problem at resonance~
$$
\left\{\begin{array}{ll}
v''(t)=f(t,v(t)),~~\ \ \ t\in 0,T],\\2ex]
v^{(i)}(0)-v^{(i)}(T)=0 ,\ \ \ i=0,1,2,
\end{array}
\right.\eqno
$$
where~$f: 0,T]\times \mathbb{R}\rightarrow \mathbb{R}$~is continuous and bounded. |
| |
| Keywords: | Lyapunov-Schmidt procedure ~Connected set ~Disordered lower and upper solutions ~Resonance ~ Existence |
| 本文献已被 CNKI 等数据库收录！ |
| 点击此处可从《四川大学学报(自然科学版)》浏览原始摘要信息 |
| 点击此处可从《四川大学学报(自然科学版)》下载免费的PDF全文 |
|
