On meromorphic solutions of certain type of difference equations

Abstract

‎We mainly discuss the existence of meromorphic (entire) solutions of‎ <br />‎certain type of non-linear difference equation of the form‎: <br />‎$f(z)^m+P(z)f(z+c)^n=Q(z)$‎, ‎which is a supplement of previous‎ <br />‎results in [K‎. ‎Liu‎, ‎L. Z‎. ‎Yang and X‎. ‎L‎. ‎Liu‎, ‎Existence of entire solutions of nonlinear difference‎ <br />‎equations‎, ‎Czechoslovak Math. J. 61 (2011)‎, no. 2, ‎565--576‎, and X‎. ‎G‎. ‎Qi‎, <br />‎Value distribution and uniqueness of difference polynomials and‎ <br />‎entire solutions of difference equations‎, ‎ Ann‎. ‎Polon‎. ‎Math.