Linear Differential Equations on the Complex Plane

1982 ◽  
Vol 89 (4) ◽  
pp. 244
Author(s):  
A. K. Bose
Keyword(s):  
Differential Equations ◽  
Complex Plane ◽  
Linear Differential Equations ◽  
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.

LOCALISATION OF LINEAR DIFFERENTIAL EQUATIONS IN THE UNIT DISC BY A CONFORMAL MAP

2015 ◽  
Vol 93 (2) ◽  
pp. 260-271
Author(s):  
JUHA-MATTI HUUSKO
Keyword(s):  
Differential Equations ◽  
Lower Bounds ◽  
Complex Plane ◽  
Exponential Growth ◽  
Unit Disc ◽  
Linear Differential Equations ◽  
Conformal Map ◽  
Conformal Maps ◽  
Linear Differential ◽  
Growth Of Solutions

We obtain lower bounds for the growth of solutions of higher order linear differential equations, with coefficients analytic in the unit disc of the complex plane, by localising the equations via conformal maps and applying known results for the unit disc. As an example, we study equations in which the coefficients have a certain explicit exponential growth at one point on the boundary of the unit disc and consider the iterated $M$-order of solutions.

scholarly journals An elementary inequality in function theory

1969 ◽  
Vol 10 (2) ◽  
pp. 162-168 ◽  
Author(s):  
W. N. Everitt
Keyword(s):  
Hilbert Space ◽  
Differential Equations ◽  
Real Axis ◽  
Complex Plane ◽  
Analytic Functions ◽  
Function Theory ◽  
Linear Differential Equations ◽  
Linear Differential ◽  
Elementary Inequality ◽  
Adjoint Operators

In the theory of self-adjoint operators in Hilbert space and of formally self-adjoint linear differential equations there are many situations involving analytic functions on the complex plane whose singularities are confined to the real axis and where the growth of the function at such singular points is strictly limited.

scholarly journals GROWTH OF \(\varphi\)–ORDER SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS WITH MEROMORPHIC COEFFICIENTS ON THE COMPLEX PLANE

2020 ◽  
Vol 6 (1) ◽  
pp. 95
Author(s):  
Mohamed Abdelhak Kara ◽  
Benharrat Belaïdi
Keyword(s):  
Differential Equations ◽  
Complex Plane ◽  
Higher Order ◽  
Linear Differential Equations ◽  
Order Linear ◽  
Linear Differential ◽  
Growth Of Solutions

In this paper, we study the growth of solutions of higher order linear differential equations with meromorphic coefficients of \(\varphi\)-order on the complex plane. By considering the concepts of \(\varphi\)-order and \(\varphi \)-type, we will extend and improve many previous results due to Chyzhykov–Semochko, Belaïdi, Cao–Xu–Chen, Kinnunen.

Sign in / Sign up

Export Citation Format

Share Document