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.
