Some results concerning meromorphic solutions for the Pielou logistic equation (Q2305654)

The Pielou logistic equation \[ x_{n+1} = \frac{\alpha x_n}{1+\beta x_n}, \] where \(\alpha>1\) and \(\beta>0\), is a discrete version of the logistic equation. Here the authors consider the value distribution of transcendental finite-order meromorphic solutions \(y(z)\) of the equation \[ y(z+1) = \frac{R(z)y(z)}{Q(z)+P(z) y(z)}, \] where \(P(z)\), \(Q(z)\) and \(R(z)\) are complex polynomials that are not identically zero. This equation is a version of the Pielou logistic equation embedded into the complex plane. The authors obtain estimates for the exponent of convergence of \(y(z+n)-y(z)\), \(y(z+1)-y(z)-a(z)\) and \(\frac{y(z+1)-y(z)}{y(z)}-a(z)\), where \(a(z)\) is an entire function of order strictly less than one.