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In this paper, we give some results about of the growth of transcendental meromorphic solutions of linear differential equations f(k) + Σj=0k-1 (Dj (z)+Aj(z) ePj(z)+Bj eQj(z)) f(j)= F, where Aj(z) (≠0), Bj (z) (≠0) and Dj (z) (j = 0,1,...,k-1) are meromorphic functions with finite order. Pj (z) = aj,nzn +...+ aj,o and Qj (z) = bj,nzn +...+bj,o (j=0,...,k-1) are nonconstant polynomials, aj,o.....aj,n, bj,o,....bj,a (j = 0,1,...,k-1) are complex numbers. Under some conditions, we prove that the hyper-order of every transcendental meromorphic solution of the above equation and of its corresponding homogeneous equation coincides with n. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the order and the hyper-order of growth of solutions of the linear differential equation where n≥2 is an integer, Aj (z) (≢0) (j = 1,2) are entire functions with max {σ A(j) : (j = 1,2} < 1, Q (z) = qmzm + ... + q1z + q0 is a nonoonstant polynomial and a1, a2 are complex numbers. Under some conditions, we prove that every solution f (z) ≢ 0 of the above equation is of infinite order and hyper-order 1.

The purpose of this paper is the study of the growth of solutions of higher order linear differential equations... [ABSTRACT FROM AUTHOR]

In this paper, we investigate the growth of meromorphic solutions of the linear differential equation f(k) + hk-1 (z)ePk-1(z) f(k-1) + ... + h0(z)eP0(z) f=0 where k ≥ 2 is an integer, Pj(z) (j = 0, 1, ..., k -- 1) are nonconstant polynomials and hj(z) are meromorphic functions. Under some conditions, we determine the hyper-order of these solutions. We also consider nonhomogeneous linear differential equations. [ABSTRACT FROM AUTHOR]

In this paper, we study the order of growth of solutions to the non-homogeneous linear differential equation f(k) + Ak-1eazf(k-1) + ... + A1eazf' + A0eazf = F1eaz + F2ebz, where Aj (z) (≢ 0) (j = 0, 1, ..., k - 1), Fj (z) (&#8802 0) (j = 1, 2) are entire functions and a, b are complex numbers such that ab (a - b) ≠ 0. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the growth and fixed points of meromorphic solutions and their derivatives to complex higher order linear differential equations whose coefficients are meromorphic functions. Our results extend the previous results due to Peng and Chen, Xu and Zhang and others. [ABSTRACT FROM AUTHOR]

We investigate the growth of meromorphic solutions of homogeneous and nonhomogeneous higher order linear differential equations f(k) + k-1 Σj=1 Ajf(j) + A0f = 0 (k ≥ 2), f(k) + k-1 Σj=1 Ajf(j) + A0f = Ak (k ≥ 2), where Aj (z) (j = 0, 1, . . . , k) are meromorphic functions with finite order. Under some conditions on the coefficients, we show that all meromorphic solutions f ≢ 0 of the above equations have an infinite order and infinite lower order. Furthermore, we give some estimates of their hyper-order, exponent and hyper-exponent of convergence of distinct zeros. We improve the results due to Kwon; Chen and Yang; Belaïdi; Chen; Shen and Xu. [ABSTRACT FROM AUTHOR]

In this paper, we mainly consider the growth and the oscillation of solutions of the second order nonhomogeneous linear differential equations ... where P (z), Q(z) are nonconstant polynomials such that deg (P) ≠ deg(Q) and hj (z) ... 0 (j = 0, 1), F (z) are meromorphic functions of finite order having only finitely many poles such that ρ (h0)

In this paper, we study the growth and the oscillation of solutions of linear difference equations with meromorphic coefficients. Also, we investigate the growth of difference polynomials generated by meromorphic solutions of some difference equations. We improve and generalize some results due to Z. X. Chen, I. Laine and C. C. Yang. [ABSTRACT FROM AUTHOR]

In this article, we discuss the order and hyper-order of the linear differential equation..., where Aj (z), Bj (z), Dj (z) are entire functions (... 0) and a1; a2; dj are complex numbers (≠ 0), and bj are real numbers. Under certain conditions, we prove that every solution f ... 0 of the above equation is of infinite order. Then, we obtain an estimate of the hyper-order. Finally, we give an estimate of the exponent of convergence for distinct zeros of the functions f(j) - φ (j = 0, 1, 2), where φ is an entire function (... 0) and of order σ(φ) < 1, while the solution f of the differential equation is of infinite order. Our results extend the previous results due to Chen, Peng and Chen and others. [ABSTRACT FROM AUTHOR]

In this paper, we will give sufficient conditions to obtain new estimates about the order of growth and the type of meromorphic functions in the unit disc Δ ={z ∊ ℂ :∣ z ∣ < 1} we give also some examples to explain the sharpness of these estimations. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate the growth of solutions of some higher order linear differential equations. We find conditions on the coefficients which will guarantee the existence of an asymptotic value for a transcendental entire solution of finite order and its derivatives. [ABSTRACT FROM AUTHOR]

This paper is devoted to studying the growth and the oscillation of solutions of the second order non-homogeneous linear difierential equation fn + A1 (z) eP(z)f' + A0 (z) eQ(z) f = F, where P (z), Q(z) are nonconstant polynomials such that deg P = degQ = n and Aj (z) (≢ 0) (j = 0, 1), F (z) are entire functions with maxf{ρ (Aj) : j = 0, 1} < n. We also investigate the relationship between small functions and difierential polynomials gf (z) = d2n + d10 + 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 ρ (dj) < n(j = 0, 1, 2) generated by solutions of the above equation. AMS subject classifications: 34M10, 30D35. [ABSTRACT FROM AUTHOR]

In this paper we discuss the growth of solutions of the higher order nonhomogeneous linear differential equation where a, b are complex constants that satisfy ab( a − b) ≠ 0 and A( z) ( j = 0, 1, ..., k − 1), D ( z) ( j = 0, 1), F( z) are entire functions with max{ ϱ( A ) ( j = 0, 1, ..., k − 1), ϱ( D) ( j = 0, 1) < 1. We also investigate the relationship between small functions and the solutions of the above equation. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the order and the hyper-order of solutions of the linear differential equation f(k) + Dk-1 + Bk-1ebk-1z f(k-1) + ... + D1 + B1eb1z f' +(D0 + A1ea1z + A2ea2z) f = 0, where Aj (z) (≢ 0) (j = 1, 2), Bl (z) (≢ 0) (l = 1, ..., k - 1), Dm (m = 0, ..., k - 1) are entire functions with max{σ (Aj), σ (Bl), σ (Dm)} < 1, a1, a2, bl (l = 1, ..., k - 1) are complex numbers. Under some conditions, we prove that every solution f (z) ≢ 0 of the above equation is of infinite order and with hyper-order 1. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the growth and the complex oscillation theory of the linear differential equation f(k) + Ak-1 f(k-1) + ߪ +A1f′ + A0f = F, where A0,A1, ߪ Ak-1, F ≢ 0 are entire functions. We also investigate the relation between the solutions of a pair non-homogeneous linear differential equations. We improve some results due to the author, S. Abbas and Z. X. Chen, S. A. Gao. [ABSTRACT FROM AUTHOR]