Growth and oscillation related to a second order linear differential equation

Abstract

This paper is devoted to studying the growth and the oscillation of solutions of the second order non-homogeneous linear di erential 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 (z) are entire functions with maxf (Aj) : j = 0; 1g < n. We also investigate the relationship between small functions and di erential polynomials gf (z) = d2f00 + d1f0 + d0f, where d0 (z) ; d1 (z) ; d2 (z) are entire functions such that at least one of d0; d1; d2 does not vanish identically with (dj) < n(j = 0; 1; 2) generated by solutions of the above equation.