一类非线性差分方程的伪概周期解

讨论了非线性差分方程x(n)=∑ⁿ_{k=-SymboleB@}α(n,n-k)f(k,x(k))+h(n,x(n)),n∈Z的伪概周期解的存在性,其中α:Z×Z⁺→R⁺,h:Z×R⁺→R⁺和f:Z×R⁺→R⁺.通过2个例子说明定理1中的4个条件是可以实现的.

The Pseudo Almost Periodic Type Solutions to a Class of Nonlinear Difference Equations

The existence theorem of pseudo almost periodic solutions to difference equationsx(n)=∑ⁿ_{k=- SymboleB@} α(n,n-k)f(k,x(k))+h(n,x(n)),n∈Zis established,where α:Z×Z⁺→R⁺,h:Z×R⁺→R⁺and f:Z×R⁺→R⁺.In addition,in order to illustrate the four conditions in Theorem 1 that are achievable,two examples is given to point out that the studied equation is a special case of the equation.