On the convergence of generalized power series solutions of q-difference equations [PDF]
Aequationes Mathematicae, 2021 A sufficient condition for the convergence of a generalized formal power series solution to an algebraic q-difference equation is provided. The main result leans on a geometric property related to the semi-group of (complex) power exponents of such a ...
Alberto Lastra
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Entire solutions for several complex partial differential-difference equations of Fermat type in ℂ2
Open Mathematics, 2021 By utilizing the Nevanlinna theory of meromorphic functions in several complex variables, we mainly investigate the existence and the forms of entire solutions for the partial differential-difference equation of Fermat type α∂f(z1,z2)∂z1+β∂f(z1,z2)∂z2m+f(
Gui Xian Min +3 more
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Open Mathematics, 2023 Our purpose in this article is to describe the solutions of several product-type nonlinear partial differential equations (PDEs) (a1u+b1uz1+c1uz2)(a2u+b2uz1+c2uz2)=1,\left({a}_{1}u+{b}_{1}{u}_{{z}_{1}}+{c}_{1}{u}_{{z}_{2}})\left({a}_{2}u+{b}_{2}{u}_{{z}_{
Xu Yi Hui +3 more
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Demonstratio Mathematica, 2023 In this article, we investigate the existence and the precise form of finite-order transcendental entire solutions of some system of Fermat-type quadratic binomial and trinomial shift equations in Cn{{\mathbb{C}}}^{n}. Our results are the generalizations
Haldar Goutam, Banerjee Abhijit
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The forbidden set, solvability and stability of a circular system of complex Riccati type difference equations [PDF]
, 2023 In this paper, the circular system of Riccati type complex difference equations of the form $ u_{n+1}^{(j)} = \frac{a_ju_n^{(j-1)}+b_j}{c_ju_n^{(j-1)}+d_j}, \; n = 0, 1, 2, \cdots, \; j = 1, 2, \cdots, k, $ where $ u_n^{(0)}: = u_n^{(k)} $ for
George L. Karakostas
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Elementary exact calculations of degree growth and entropy for discrete equations [PDF]
, 2017 Second-order discrete equations are studied over the field of rational functions C(z)C(z), where z is a variable not appearing in the equation. The exact degree of each iterate as a function of z can be calculated easily using the standard calculations ...
Halburd, RG
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Special functions created by Borel-Laplace transform of Henon map [PDF]
, 2011 Electronic Research Announcements in Mathematical Sciences.
Hiraide, Koichi, Matsuoka, Chihiro
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On transcendental entire solution of Fermat-type trinomial and binomial equations under restricted hyper-order [PDF]
, 2023 In this paper we are focusing on finding the transcendental entire solution of Fermat-type trinomial and binomial equations, by restricting the hyper-order to be less than one.
Banerjee, Abhijit, Sarkar, Jhuma
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New class of practically solvable systems of difference equations of hyperbolic-cotangent-type [PDF]
, 2020 The systems of difference equations $$x_{n+1}=\frac{u_nv_{n-2}+a}{u_n+v_{n-2}},\quad y_{n+1}=\frac{w_ns_{n-2}+a}{w_n+s_{n-2}},\quad n\in\mathbb{N}_0,$$ where $a, u_0, w_0, v_j, s_j$ $j=-2,-1,0,$ are complex numbers, and the sequences $u_n$, $v_n,$ $w_n$,
Stevic, Stevo
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Solvability of a product-type system of difference equations with six parameters
Advances in Nonlinear Analysis, 2016 Closed form formulas for well-defined complex-valued solutions to a product-type system of difference equations of interest with six parameters are presented. The form of the solutions is described in detail in terms of the parameters and initial values.
Stević Stevo
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