Some properties of meromorphic solutions of higher order linear difference equations

Abstract

In this paper, we investigate the growth of solutions of the linear difference equations Ak(z) f (z+ ck)+Ak−1(z) f (z+ ck−1)+ · · ·+A1(z) f (z+ c1)+A0(z) f (z) = 0, Ak(z) f (z+ ck)+Ak−1(z) f (z+ ck−1)+ · · ·+A1(z) f (z+ c1)+A0(z) f (z) = F(z), where Ak(z), · · · ,A0(z), F(z)(̸≡ 0) are entire functions and ck, · · · ,c1 are distinct non-zero complex numbers. We extend some precedent results due to Liu and Mao [15].