| 路艳琼,马如云,卢博.带参数的一阶泛函差分方程的定号周期解[J].数学研究及应用,2018,38(4):384~392 |
| 带参数的一阶泛函差分方程的定号周期解 |
| One-Signed Periodic Solutions of First-Order Functional Difference Equations with Parameter |
| 投稿时间：2017-09-05 修订日期：2018-05-17 |
| DOI：10.3770/j.issn:2095-2651.2018.04.006 |
| 中文关键词: |
| 英文关键词:one-signed periodic solutions existence functional difference equations bifurcation from infinity |
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| 英文摘要: |
| In this paper, the authors obtain the existence of one-signed periodic solutions of the first-order functional difference equation $$\Delta u(n)=a(n)u(n)-\lambda b(n) f(u(n-\tau(n))),~~n\in\mathbb{Z}$$ by using global bifurcation techniques, where $a,b:\mathbb{Z}\rightarrow[0,\infty)$ are $T$-periodic functions with $\sum_{n=1}^{T}a(n)>0$, $\sum_{n=1}^{T}b(n)>0$; $\tau:\mathbb{Z}\to\mathbb{Z}$ is $T$-periodic function, $\lambda>0$ is a parameter; $f\in C(\mathbb{R},\mathbb{R})$ and there exist two constants $s_2<00$ for $s\in(0,s_1)\cup(s_1,\infty)$, and $f(s)<0$ for $s\in(-\infty,s_2)\cup(s_2,0)$. |
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