Growth of solutions and oscillation of differential polynomials generated by some complex linear differential equations

Abstract

This paper is devoted to studying the growth and the oscillation of solutions of the second order non-homogeneous linear differential equation f00 + A1(z)eP(z) f0 + A0(z)eQ(z) f = F; where P(z), Q(z) are nonconstant polynomials such that deg P = degQ = n and Aj (z) (6´ 0) (j = 0; 1), F 6´ 0 are entire functions with ½(Aj ) < n (j = 0; 1). We also investigate the relationship between small functions and differential polynomials gf (z) = d2f00 + d1f0 + d0f, where d0(z), d1(z), d2(z) are entire functions that are not all equal to zero with ½(dj ) < n (j = 0; 1; 2) generated by solutions of the above equation.