Growth and zeros of meromorphic solution of some linear difference equations

In this paper, we study growth and zeros of linear difference equationsPn(z)f(z+n)+⋯+P1(z)f(z+1)+P0(z)f(z)=F(z)Pn(z)f(z+n)+⋯+P1(z)f(z+1)+P0(z)f(z)=F(z) where F(z),Pn(z),…,P0(z)F(z),Pn(z),…,P0(z) are polynomials with FPnP0≢0FPnP0≢0 and satisfy deg(Pn+⋯+P0)=max{degPj:j=0,…,n}⩾1. The corresponding homogeneous equation of the above equation is also investigated.