On the convergence of generalized power series solutions of q-difference equations
نویسندگان
چکیده
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 geometric property related semi-group (complex) exponents such series. This corresponds situation in which small divisors phenomenon does not arise. Some examples illustrating cases where obtained can or cannot be applied are also depicted.
منابع مشابه
q-Hypergeometric solutions of q-difference equations
We present algorithm qHyper for finding all solutions y(x) of a linear homogeneous q-difference equation, such that y(qx) = r(x)y(x) where r(x) is a rational function of x. Applications include construction of basic hypergeometric series solutions, and definite q-hypergeometric summation in closed form. ∗The research described in this publication was made possible in part by Grant J12100 from t...
متن کاملOn 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...
متن کاملGeneralized power series solutions to linear partial differential equations
Let Θ = C[e−x1 , . . . , e−xn ][∂1, . . . , ∂n] and S = C[x1, . . . , xn][[eCx1+···+Cxn ]], where C is an effective field and xN 1 · · · x N n e Cx1+···+Cxn and S are given a suitable asymptotic ordering 4. Consider the mapping L : S → Sl ; f 7→ (L1 f, . . . , Ll f ), where L1, . . . , Ll ∈ Θ . For g = (g1, . . . , gl ) ∈ Sl L = im L , it is natural to ask how to solve the system L f = g. In th...
متن کاملInverse Factorial-series Solutions of Difference Equations
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...
متن کاملOn Convergence of Difference Schemes for IBVP for Quasilinear Parabolic Equations with Generalized Solutions
For initial boundary value problem (IBVP) for onedimensional quasilinear parabolic equations with generalized solutions an usual linearized difference scheme is constructed. The uniform parabolicity condition 0 < k 1 ≤ k(u) ≤ k 2 is assumed to be fulfilled for the sign alternating solution u(x, t) ∈ ¯ D(u) only in the domain of exact solution values (unbounded nonlinearity). On the basis of the...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Aequationes Mathematicae
سال: 2021
ISSN: ['0001-9054', '1420-8903']
DOI: https://doi.org/10.1007/s00010-021-00817-7