On the growth of solutions of $f”+gf’+hf=0$

Abstract

Abstract. Suppose g and h are entire functions with the order of h less than the order of g . If the order of g does not exceed j , it is shown that every (necessarily entire) nonconstant solution / of the differential equation f" + gf + hf = 0 has infinite order. This result extends previous work of Ozawa and Gundersen.

The radial oscillation of entire solutions of complex differential equations

“…where A(z), B(z) and F (z) are entire in C. Since 1982, great progress have been achieved on the global theory of (1), see [14,6,7,10,11,13,2,3]. However, the research on the properties of solutions in an angle is not so active.…”

On the growth of solutions of a class of higher order linear differential equations with coefficients having the same order

“…It is well known that if either σ (B) < σ (A) or σ (A) < σ (B) 1/2, then every solution f ≡ 0 of (1.1) is of infinite order (see [9,13]). For the case σ (A) < σ (B) and σ (B) > 1/2, many authors have studied the problem.…”

On the growth of solutions to the complex differential equation f″ + Af′ + Bf = 0

“…There has been much work on this subject. For example, it follows from the work by Gunderson [10], Hellerstein, Miles and Rossi [12] that if A(z) and B(z) are entire functions with ρ(A) < ρ(B); or if A(z) is a polynomial, and B(z) is transcendental; or if ρ(B) < ρ(A) 1 2 , then every solution f ≡ 0 of the equation (1.1) has infinite order.…”