A boundary value problem associated with the difference equation with advanced argument *Δ(anΦ(Δxn))+bnΦ(xn+p)=0,n≥1 is presented, where Φ(u) = |u|αsgn u, α > 0, p is a positive integer and the sequences a, b, are positive. We deal with a particular type of decaying solution of (*), that is the so-called intermediate solution (see below for the definition). In particular, we prove the existence of this type of solution for (*) by reducing it to a suitable boundary value problem associated with a difference equation without deviating argument. Our approach is based on a fixed-point result for difference equations, which originates from existing ones stated in the continuous case. Some examples and suggestions for future research complete the paper. This article is part of the theme issue ‘Topological degree and fixed point theories in differential and difference equations’.

中文翻译：

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差分方程衰减解的定点法

提出了一个与带有高级参数*Δ(anΦ(Δxn))+bnΦ(xn+p)=0,n≥1的差分方程相关的边值问题，其中Φ(u) = |u|αsgn u, α > 0，p为正整数，序列a、b为正数。我们处理（*）的一种特定类型的衰减解，即所谓的中间解（定义见下文）。特别是，我们通过将 (*) 简化为与差分方程相关的合适边值问题而不偏离论证来证明这种类型的解的存在。我们的方法基于差分方程的定点结果，该结果源自连续情况下的现有方程。一些示例和对未来研究的建议完善了本文。