论文标题
衰减差方程解决方案解决方案的定点方法
A fixed-point approach for decaying solutions of difference equations
论文作者
论文摘要
与高级参数\差异方程相关的边界值问题\ begin {qore} \ label {*}δ\ bigl（a_ {n}φ（δx_{n}）\ bigr）+b_ {n}φ（x_ {n+p}）呈现的，其中$φ（u）= | u |^α$ sgn $ u，$ $ $ $ a> 0，p $是一个正整数，序列$ a，b，$是正面的。我们处理（\ ref {*}）的一种特定类型的衰减解决方案，即所谓的中间解决方案（定义，请参见下文）。特别是，我们通过将其简化为与差异方程相关的合适边界价值问题，而不会偏离参数，证明了（\ ref {*}）的这些类型的解决方案的存在。我们的方法基于差方程的固定点结果，该方程源自连续情况下的现有情况。对未来研究的一些示例和建议完成了本文。
A boundary value problem associated to the difference equation with advanced argument \begin{equation} \label{*}Δ\bigl (a_{n}Φ(Δx_{n})\bigr)+b_{n}Φ(x_{n+p} )=0,\ \ n\geq1 \tag{$*$} \end{equation} is presented, where $Φ(u)=|u|^α$sgn $u,$ $α>0,p$ is a positive integer and the sequences $a,b,$ are positive. We deal with a particular type of decaying solutions of (\ref{*}), that is the so-called intermediate solutions (see below for the definition) . In particular, we prove the existence of these type of solutions for (\ref{*}) by reducing it to a suitable boundary value problem associated to 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 researches complete the paper.
