Meromorphic solutions of non‐linear differential equations of the form fn+Pfalse(z,ffalse)=h are investigated, where n≥2 is an integer, h is a meromorphic function, and P(z,f) is differential polynomial in f and its derivatives with small functions as its coefficients. In the existing literature this equation has been studied in the case when h has the particular form hfalse(zfalse)=p1false(zfalse)eα1false(zfalse)+p2false(zfalse)eα2false(zfalse), where p1,p2 are small functions of f and α1,α2 are entire functions. In such a case the order of h is either a positive integer or equal to infinity. In this article it is assumed that h is a meromorphic solution of the linear differential equation h′′+r1false(zfalse)h′+r0false(zfalse)h=r2false(zfalse) with rational coefficients r0,r1,r2, and hence the order of h is a rational number. Recent results by Liao–Yang–Zhang (2013) and Liao (2015) follow as special cases of the main results.
In this paper, we investigate the complex higher order linear differential equations in which the coefficients are analytic functions in the unit disc of [p, q]-order. We obtain several theorems about the growth and oscillation of solutions of differential equations.
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