带参数的一阶泛函差分方程的定号周期解

In this paper,the authors obtain the existence of one-signed periodic solutions of the first-order functional difference equation ?u(n) = a(n)u(n)-λb(n)f(u(n-τ(n))),n ∈ Z by using global bifurcation techniques,where a,b:Z → 0,∞) are T-periodic functions with ∑T n=1 a(n) 0,∑T n=1 b(n) 0;τ:Z → Z is T-periodic function,λ 0 is a parameter;f ∈ C(R,R) and there exist two constants s_2 0 s_1 such that f(s_2) = f(0) = f(s_1) = 0,f(s) 0 for s ∈(0,s_1) ∪(s_1,∞),and f(s) 0 for s ∈(-∞,s_2) ∪(s_2,0).

One-Signed Periodic Solutions of First-Order Functional Difference Equations with Parameter

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 $a,b:\mathbb{Z}\rightarrow0,\infty)$ 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 $s\in(-\infty,s_2)\cup(s_2,0)$.