Existence Of Meromorphic Solutions Research Articles

Existence and convergence results of meromorphic solutions to the equilibrium system with angular velocity

We study the equilibrium system with angular velocity for the prey. This system is a generalization of the two-species equilibrium model with Neumann type boundary condition. Firstly, we consider the asymptotical stability of equilibrium points to the system of ordinary differential equations type. Then, the existence of meromorphic solutions and the stability of equilibrium points to the system of weakly coupled meromorphic type are discussed. Finally, the existence of nonnegative meromorphic solutions to the system of strongly coupled meromorphic type is investigated, and the asymptotic stability of unique positive equilibrium point of the system is proved by constructing meromorphic functions.

The Existence of Meromorphic Solutions of Some Types of Systems of Complex Functional Equations

We investigate the existence of transcendental meromorphic solutions of some types of systems of complex functional equations and obtain some results about the existence of meromorphic solutions of such systems. Our results are improvement of the previous theorems given by Gao, Xu, and Zheng, and our examples show that our results are sharp to some extent.

All meromorphic solutions of some algebraic differential equations and their applications

Abstract In this paper, we employ Nevanlinna’s value distribution theory to investigate the existence of meromorphic solutions of some algebraic differential equations. We obtain the representations of all meromorphic solutions of certain algebraic differential equations with constant coefficients and dominant term. Many results are the corollaries of our result, and we will give the complex method to find all traveling wave exact solutions of corresponding partial differential equations. As an example, we obtain all meromorphic solutions of the Kuramoto-Sivashinsky equation by using our complex method. Our results show that the complex method provides a powerful mathematical tool for solving great many nonlinear partial differential equations in mathematical physics. MSC:30D35, 34A05.

Existence of meromorphic solutions of some higher order linear differential equations

This article discusses the problems on the existence of meromorphic solutions of some higher order linear differential equations with meromorphic coefficients. Some nice results are obtained. And these results perfect the complex oscillation theory of meromorphic solutions of linear differential equations.

On the asymptotics of meromorphic solutions for nonlinear Riemann–Hilbert problems

This paper is devoted to a global existence theorem of meromorphic solutions of the form Z(z)=Zo(z)+R(z) of a nonlinear Riemann–Hilbert problem (RHP) for multiply connected domains Gq(q[ges ]1), where Zo(z) is the singular part of the solution, R(z) is the regular part which is a holomorphic solution of some appropriate nonlinear RHP for Gq(q[ges ]1). Under appropriate conditions on the characteristics of both the singular part Zo(z) (number of poles) and regular part (winding number) we prove the existence of meromorphic solutions Z(z) of the form Z(z)=Zo(z)+R(z). The proof is based on a special construction of the singular part Zo(z) and an adequate formulation of Newton's method for the regular part R(z).

On the existence of meromorphic solutions of differential equations having arbitarily rapid growth.

On the existence of meromorphic solutions of differential equations having arbitarily rapid growth.