On the growth of solutions of difference equations in ultrametric fields

Let KK be a complete ultrametric algebraically closed field. In this article, we consider the functional equations ∑i=0sgi(x)y(qix)=h(x) and ∑i=0sgi(x)y(x+i)=h(x), where qq is an element of KK such that 0<|q|<10<|q|<1  and  h(x),g0(x),…,gs(x)(s≥1) are meromorphic functions in all KK such that g0(x)gs(x)≢0g0(x)gs(x)≢0. For each of the above equations, we study the growth of meromorphic solutions y=f(x)y=f(x) according to that of the functions g0,…,gsg0,…,gs and hh.