The growth of meromorphic solutions for q−difference Painlevé IV equation

Abstract

We consider meromorphic solutions of q−difference Painlevé IV equation(f(qz)+f(z))(f(z)+f(z/q))=P(z,f(z))Q(z,f(z)), where P(z,f(z)) and Q(z,f(z)) are polynomials in f having polynomial coefficients and no common roots, and q∈C∖{0}. We investigate the growth of transcendental meromorphic solutions of q−difference Painlevé IV equation and find lower bounds for their characteristic functions for transcendental meromorphic solutions of such equation for the case m=degf⁡(P)−degf⁡(Q)≥3.