Exponential polynomials as solutions of certain nonlinear difference equations |
| |
Authors: | Zhi Tao Wen Janne Heittokangas Ilpo Lain |
| |
Institution: | 1. Department of Physics and Mathematics, University of Eastern Finland, P.O. Box 111, 80101, Joensuu, Finland
|
| |
Abstract: | Recently, C.-.C. Yang and I. Laine have investigated finite order entire solutions f of nonlinear differential-difference equations of the form f n + L(z, f) = h, where n ≥ 2 is an integer. In particular, it is known that the equation f(z)2 +q(z)f(z +1) = p(z), where p(z),q(z) are polynomials, has no transcendental entire solutions of finite order. Assuming that Q(z) is also a polynomial and c ∈ ?, equations of the form f(z) n +q(z)e Q(z) f(z +c) = p(z) do posses finite order entire solutions. A classification of these solutions in terms of growth and zero distribution will be given. In particular, it is shown that any exponential polynomial solution must reduce to a rather specific form. This reasoning relies on an earlier paper due to N. Steinmetz. |
| |
Keywords: | Convex hull difference equation entire solution exponential polynomial Nevanlinna theory |
本文献已被 CNKI 维普 SpringerLink 等数据库收录! |
|