scholarly journals Three results in the value-distribution theory of solutions of linear differential equations

1986 ◽  
Vol 9 (2) ◽  
pp. 225-240 ◽  
Author(s):  
Steven B. Bank
Keyword(s):  
Differential Equations ◽  
Distribution Theory ◽  
Value Distribution ◽  
Linear Differential Equations ◽  
Value Distribution Theory ◽  
Linear Differential

Entire solutions of certain type of non-linear differential equations

2020 ◽  
Vol 70 (1) ◽  
pp. 87-94
Author(s):  
Bo Xue
Keyword(s):  
Differential Equations ◽  
Complex Plane ◽  
Meromorphic Functions ◽  
Nonlinear Differential Equations ◽  
Differential Polynomial ◽  
Value Distribution ◽  
Linear Differential Equations ◽  
Entire Solutions ◽  
Value Distribution Theory ◽  
Linear Differential

AbstractUtilizing Nevanlinna’s value distribution theory of meromorphic functions, we study transcendental entire solutions of the following type nonlinear differential equations in the complex plane$$\begin{array}{} \displaystyle f^{n}(z)+P(z,f,f',\ldots,f^{(t)})=P_{1}\text{e}^{\alpha_{1}z}+P_{2}\text{e}^{\alpha_{2}z}+P_{3}\text{e}^{\alpha_{3}z}, \end{array}$$where Pj and αi are nonzero constants for j = 1, 2, 3, such that |α1| > |α2| > |α3| and P(z, f, f′, …, f(t) is an algebraic differential polynomial in f(z) of degree no greater than n – 1.

scholarly journals Growth of Logarithmic Derivatives and Their Applications in Complex Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Zinelâabidine Latreuch ◽  
Benharrat Belaïdi
Keyword(s):  
Differential Equations ◽  
Entire Functions ◽  
Value Distribution ◽  
Linear Differential Equations ◽  
Differential Polynomials ◽  
Complex Differential Equations ◽  
Linear Differential ◽  
Logarithmic Derivatives

We continue the study of the behavior of the growth of logarithmic derivatives. In fact, we prove some relations between the value distribution of solutions of linear differential equations and growth of their logarithmic derivatives. We also give an estimate of the growth of the quotient of two differential polynomials generated by solutions of the equation f″+A(z)f′+B(z)f=0, where A(z) and B(z) are entire functions.

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