论文标题
在一类功能差方程中：明确的解决方案，渐近行为和应用
On a class of functional difference equations: explicit solutions, asymptotic behavior and applications
论文作者
论文摘要
对于$ν\在[0,1] $和一个复杂的参数$σ，$ $ re \，σ> 0，$我们讨论一个线性不均匀的功能差方程，并在复杂的平面$ z \ in \ mathbb {c} $上具有可变系数（a_ {1}σ+a_ {2}σ^ν）\ Mathcal {y}（z+β，σ）-Ω（z）\ Mathcal {y}（z，z，σ）= \ m缩$ω（z）$和$ \ mathbb {f}（z）$具有复杂的功能，而$ a_ {1} $和$ a_ {2} $给出了实际的非负数。在给定函数和参数的适当条件下，我们构建了方程式的显式解决方案，并将其渐近行为描述为$ | z | \ to +\ to +\ infty $。然后讨论了功能差方程理论的某些应用以及对非平滑域中次扩散控制的边界价值问题理论的应用。
For $ν\in[0,1]$ and a complex parameter $σ,$ $Re\, σ>0,$ we discuss a linear inhomogeneous functional difference equation with variable coefficients on a complex plane $z\in\mathbb{C}$: \[ (a_{1}σ+a_{2}σ^ν)\mathcal{Y}(z+β,σ)-Ω(z)\mathcal{Y}(z,σ)=\mathbb F(z,σ), \quadβ\in\mathbb{R},\, β\neq 0, \] where $Ω(z)$ and $\mathbb{F}(z)$ are given complex functions, while $a_{1}$ and $a_{2}$ are given real non-negative numbers. Under suitable conditions on the given functions and parameters, we construct explicit solutions of the equation and describe their asymptotic behavior as $|z|\to +\infty$. Some applications to the theory of functional difference equations and to the theory of boundary value problems governed by subdiffusion in nonsmooth domains are then discussed.
