### Existence and global attractivity of periodic solutions to some classes of difference equations

#### Abstract

Existence and global attractivity of periodic solutions to some subclasses of the following class of difference equations

$$x_{n+1}=q_nx_n+f(n,x_n,x_{n-1},\ldots,x_{n-k}),\quad n\in N_0,$$

where $k\in N_0$, $(q_n)_{n\in N_0}$ is a $T$-periodic sequence ($T\in N$), and $f: N_0\times R^{k+1}\to R$ is a $T$-periodic function in the first variable, which for each $n\in\{0,1,\ldots, T-1\}$is continuous in other variables, are studied.

$$x_{n+1}=q_nx_n+f(n,x_n,x_{n-1},\ldots,x_{n-k}),\quad n\in N_0,$$

where $k\in N_0$, $(q_n)_{n\in N_0}$ is a $T$-periodic sequence ($T\in N$), and $f: N_0\times R^{k+1}\to R$ is a $T$-periodic function in the first variable, which for each $n\in\{0,1,\ldots, T-1\}$is continuous in other variables, are studied.

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