Došlá Zuzana, Marini Mauro, Matucci Serena
Department of Mathematics and Statistics, Masaryk University, Kotlářská 2, 61137 Brno, Czech Republic.
Department of Mathematics and Computer Science 'Ulisse Dini', University of Florence, Via di S. Marta 3, 50139 Florence, Italy.
Philos Trans A Math Phys Eng Sci. 2021 Feb 22;379(2191):20190374. doi: 10.1098/rsta.2019.0374. Epub 2021 Jan 4.
A boundary value problem associated with the difference equation with advanced argument [Formula: see text] is presented, where () = ||sgn , > 0, is a positive integer and the sequences , , 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'.
提出了一个与具有超前自变量的差分方程[公式：见正文]相关的边值问题，其中( ) = ||sgn ， > 0， 是正整数，且序列 、 、 为正。我们研究()的一种特殊类型的衰减解，即所谓的中间解（定义见下文）。特别地，我们通过将其归结为与一个无偏差自变量的差分方程相关的合适边值问题，来证明()存在这种类型的解。我们的方法基于差分方程的一个不动点结果，该结果源于连续情形下已有的结果。一些例子和对未来研究的建议完善了本文。本文是“微分和差分方程中的拓扑度和不动点理论”主题专刊的一部分。
