Solutions for Linear Differential Equations with Meromorphic Coefficients of (p,q)-order in the Plane
نویسندگان
چکیده
In this article we study the growth of meromorphic solutions of high order linear differential equations with meromorphic coefficients of (p, q)order. We extend some previous results due to Beläıdi, Cao-Xu-Chen, Kinnunen, LiuTu -Shi, and others.
منابع مشابه
Growth of solutions of linear differential equations with meromorphic coefficients of [p, q]-order
In this paper, we investigate the growth of meromorphic solutions to a complex higher order linear differential equation whose coefficients are meromorphic functions of [p, q]-orders. We get the results about the lower [p, q]-order of solutions of the equation. Moreover, we investigate the [p, q]-convergence exponent and the lower [p, q]-convergence exponent of distinct zeros of f(z)− φ(z). AMS...
متن کاملThe Oscillation on Solutions of Some Classes of Linear Differential Equations with Meromorphic Coefficients of Finite [p, q]-Order
This paper considers the oscillation on meromorphic solutions of the second-order linear differential equations with the form f'' + A(z)f = 0, where A(z) is a meromorphic function with [p, q]-order. We obtain some theorems which are the improvement and generalization of the results given by Bank and Laine, Cao and Li, Kinnunen, and others.
متن کاملGrowth of meromorphic solutions for complex difference equations of Malmquist type
In this paper, we give some necessary conditions for a complex difference equation of Malmquist type $$sum^n_{j=1}f(z+c_j)=frac{P(f(z))}{Q(f(z))},$$ where $n(in{mathbb{N}})geq{2}$, and $P(f(z))$ and $Q(f(z))$ are relatively prime polynomials in $f(z)$ with small functions as coefficients, admitting a meromorphic function of finite order. Moreover, the properties of finite o...
متن کاملOn meromorphic solutions of certain type of difference equations
We mainly discuss the existence of meromorphic (entire) solutions of certain type of non-linear difference equation of the form: $f(z)^m+P(z)f(z+c)^n=Q(z)$, which is a supplement of previous results in [K. Liu, L. Z. Yang and X. L. Liu, Existence of entire solutions of nonlinear difference equations, Czechoslovak Math. J. 61 (2011), no. 2, 565--576, and X. G. Qi...
متن کاملUniqueness of meromorphic functions ans Q-differential polynomials sharing small functions
The paper concerns interesting problems related to the field of Complex Analysis, in particular, Nevanlinna theory of meromorphic functions. We have studied certain uniqueness problem on differential polynomials of meromorphic functions sharing a small function. Outside, in this paper, we also consider the uniqueness of $q-$ shift difference - differential polynomials of mero...
متن کامل