| 高承华.一阶离散周期问题的多解性[J].数学研究及应用,2014,34(3):323~331 |
| 一阶离散周期问题的多解性 |
| Multiple Solutions for Discrete First-Order Periodic Problems |
| 投稿时间：2012-10-25 修订日期：2014-01-13 |
| DOI：10.3770/j.issn:2095-2651.2014.03.009 |
| 中文关键词: 一阶离散周期问题 Landesman-Lazer 条件 Leray-Schauder 度 分歧 存在性.hauder 度 分歧 存在性. |
| 英文关键词:discrete first-order periodic problems Landesman-Lazer type condition Leray-Schauder degree bifurcation existence. |
| 基金项目:国家自然科学基金(Grant Nos.11326127; 11101335), 甘肃省高等学校科研项目(Grant No.2013A-001),西北师范大学青年教师科研提升计划(Grant No.NWNU-LKQN-11-23). |
|
| 摘要点击次数: 2742 |
| 全文下载次数: 2077 |
| 中文摘要: |
| 设$T>1$是一个整数, $\mathbb{T}=\{0,1,2,\ldots,T-1\}$. 考虑一阶离散周期边值问题$$\Delta u(t)-a(t)u(t)=\lambda u(t)+f(u(t-\tau(t)))-h(t),~~t\in\mathbb{T},$$$$u(0)=u(T)$$ 周期解的存在性, 其中, $\Delta u(t)=u(t+1)-u(t)$,\ $a:\mathbb{T}\to\mathbb{R}$ 并且满足\ $\prod^{T-1}_{t=0}(1+a(t))=1$, $\tau:\mathbb{T}\to\mathbb{Z}$, $t-\tau(t)\in\mathbb{T}$,$t\in\mathbb{T}$, $f:\mathbb{R}\to\mathbb{R}$ 连续并且满足Landesman-Lazer条件,$h:\mathbb{T}\to\mathbb{R}$.本文所用的主要工具是Rabinowitz全局分歧定理和Leray-Schauder\ 度理论. |
| 英文摘要: |
| Let $T>1$ be an integer, $\mathbb{T}=\{0,1,2,\ldots,T-1\}$. This paper is concerned with the existence of periodic solutions of the discrete first-order periodic boundary value problems $$\Delta u(t)-a(t)u(t)=\lambda u(t)+f(u(t-\tau(t)))-h(t),~~t\in\mathbb{T},$$ $$u(0)=u(T),$$ where $\Delta u(t)=u(t+1)-u(t)$, $a:\mathbb{T}\to\mathbb{R}$ and satisfies $\prod^{T-1}_{t=0}(1+a(t))=1$, $\tau:\mathbb{T}\to\mathbb{Z}$ $t-\tau(t)\in\mathbb{T}$ for $t\in\mathbb{T}$, $f:\mathbb{R}\to\mathbb{R}$ is continuous and satisfies Landesman-Lazer type condition and $h:\mathbb{T}\to\mathbb{R}$. The proofs of our main results are based on the Rabinowitz's global bifurcation theorem and Leray-Schauder degree. |
| 查看全文 查看/发表评论 下载PDF阅读器 |
|
|
|
