Approximative solutions of difference equations
نویسندگان
چکیده
منابع مشابه
On meromorphic solutions of certain type of difference equations
We mainly discuss the existence of meromorphic (entire) solutions of certain type of non-linear difference equation of the form: $f(z)^m+P(z)f(z+c)^n=Q(z)$, which is a supplement of previous results in [K. Liu, L. Z. Yang and X. L. Liu, Existence of entire solutions of nonlinear difference equations, Czechoslovak Math. J. 61 (2011), no. 2, 565--576, and X. G. Qi...
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We obtain inverse factorial-series solutions of second-order linear difference equations with a singularity of rank one at infinity. It is shown that the Borel plane of these series is relatively simple, and that in certain cases the asymptotic expansions incorporate simple resurgence properties. Two examples are included. The second example is the large a asymptotics of the hypergeometric func...
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1 We investigate the zeros of polynomial solutions to the differential-difference equation P n+1 (x) = A n (x)P ′ n (x) + B n (x)P n (x), n = 0, 1,. .. where A n and B n are polynomials of degree at most 2 and 1 respectively. We address the question of when the zeros are real and simple and whether the zeros of polynomials of adjacent degree are interlac-ing. Our result holds for general classe...
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For a field k with an automorphism σ and a derivation δ, we introduce the notion of liouvillian solutions of linear difference-differential systems {σ(Y ) = AY, δ(Y ) = BY } over k and characterize the existence of liouvillian solutions in terms of the Galois group of the systems. We will give an algorithm to decide whether such a system has liouvillian solutions when k = C(x, t), σ(x) = x+ 1, ...
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For a field k with an automorphism σ and a derivation δ, we introduce the notion of liouvillian solutions of linear difference-differential systems {σ(Y ) = AY, δ(Y ) = BY } over k and characterize the existence of liouvillian solutions in terms of the Galois group of the systems. We will give an algorithm to decide whether such a system has liouvillian solutions when k = C(x, t), σ(x) = x + 1,...
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ژورنال
عنوان ژورنال: Electronic Journal of Qualitative Theory of Differential Equations
سال: 2014
ISSN: 1417-3875
DOI: 10.14232/ejqtde.2014.1.13