Growth of meromorphic solutions of linear difference equations without dominating coefficients

Abstract

Abstract This paper is devoted to studying the growth of meromorphic solutions of difference equation Pn(z)f(z+n)+Pn−1f(z+n−1)+⋯+P1(z)f(z+1)+P0(z)f(z)=0, $$ P_{n}{(z)}f(z+n)+P_{n-1}f(z+n-1)+\cdots +P_{1}{(z)}f(z+1)+P_{0}{(z)}f(z)=0, $$ where the coefficients Pj $P_{j}$ ( j=0,…,n $j=0,\ldots ,n$) are meromorphic functions. With some additional conditions on coefficients, we obtain precise estimates of the growth of meromorphic solutions of such an equation.

Keywords

• Complex difference equation
• Finite order
• Lower order
• Deficient value
• Wandering domain