Relations between the small functions and the solutions of certain second-order differential equations

Abstract

<p>In this paper, we investigate the relations between the small functions and the solutions, first, second derivatives, and differential polynomial of the solutions to the differential equation</p> <pre>ƒ″ + A₁e^P(z) ƒ′ + A(sub>0</sub>e^Q(z) ƒ = 0,</pre> <p>where P(z) = α_nzⁿ + ⋅⋅⋅ + α₀, Q(z) = b_nzⁿ + ⋅⋅⋅ + b₀ are polynomials with degree n (n ≥ 1), α_i, b_i (i = 0, 1,..., n), α_nb_n ≠ 0 are complex constants, A_j(z) ≢ 0 (j = 0, 1) are entire functions with σ(A_j) < n.</p>