Finite order solutions of non-homogeneous linear differential equations with entire coefficients

The growth of finite order solutions of non-homogeneous linear differential equation $f^{(k)}+A_{k-1}(z)f^{(k-1)}+\cdots+A_1(z)f'+A_0(z)f=F(z)$ is considered, where $A_j(z),~j=0,\cdots,k-1,~F(z)$ are entire functions,and there exists some $A_s(z)$ as exponentially dominating in a sector.