On growth, zeros and poles of meromorphic solutions of linear and nonlinear difference equations
The author studies the order of growth, zeros and poles of finite order meromorphic solutions of nonlinear difference equations \[ P(z) y(z+1)y(z)+Q(z)y(z)y(z-1)=H(z)\eqno{(1.1)} \] and \[ y(z+1)=\frac{R(z)y(z)}{Q(z)+P(z)y(z)},\eqno{(1.2)} \] where \(P(z), Q(z), H(z)\) and \(R(z)\) are polynomials such that \(P(z) Q(z) H(z) R(z)\not\equiv 0\). Similar results for linear difference equations related to (1.1) and (1.2) are also obtained.
scientific article; zbMATH DE number 6000062
scientific article