On a class of functional difference equations: explicit solutions, asymptotic behavior and applications
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866929283316842496 |
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| author | Vasylyeva, Nataliya |
| author_facet | Vasylyeva, Nataliya |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_06136 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On a class of functional difference equations: explicit solutions, asymptotic behavior and applications Vasylyeva, Nataliya Analysis of PDEs Complex Variables 39A06, 39B32 (Primary), 35C15, 35R11, 35R35 (Secondary) 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. |
| title | On a class of functional difference equations: explicit solutions, asymptotic behavior and applications |
| topic | Analysis of PDEs Complex Variables 39A06, 39B32 (Primary), 35C15, 35R11, 35R35 (Secondary) |
| url | https://arxiv.org/abs/2210.06136 |