Meromorphic solutions on the first order non-linear difference equations
In the paper the authors consider the first order nonlinear difference equation of the form \[C(z, f)f^{2}(z + c) + B(z, f) f(z + c) + A(z, f) = 0,\] where \(A(z, f)\), \(B(z, f)\) and \(C(z, f)\) are polynomials in \(f\) with rational coefficients. Let \(t = \deg_{f}A(z, f)\), \(n = \deg_{f}B(z, f)\) and \(m = \deg_{f}C(z, f)\). A typical result of the paper states that if the above equation admits transcendental entire solution \(f\) with hyper-order less than \(1\), then \(m \leq \max \{n - 1, t - 2\}\), \(n \leq \max \{m + 1, t - 1\}\) and \(t \leq \max\{m + 2, n + 1\}\).
scientific article; zbMATH DE number 7254986
scientific article