On the Connection Problem for Painlevé Differential Equation in View of Geometric Function Theory

Mathematics

RafidaM. Elobaid¹  RabhaW. Ibrahim²  SuzanJ. Obaiys³ 

[1] Department of General Sciences, Prince Sultan University, Riyadh 12435, Saudi Arabia;Informetrics Research Group, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam;School of Mathematical and Computer Sciences, Heriot-Watt University Malaysia, Putrajaya 62200, Malaysia;

关键词: Painlevé differential equation;    symmetric solution;    asymptotic expansion;    univalent function;    subordination and superordination;    analytic function;   

DOI  :  10.3390/math8071198

来源: DOAJ

【 摘 要 】

Asymptotic analysis is a branch of mathematical analysis that describes the limiting behavior of the function. This behavior appears when we study the solution of differential equations analytically. The recent work deals with a special class of third type of Painlevé differential equation (PV). Our aim is to find asymptotic, symmetric univalent solution of this class in a symmetric domain with respect to the real axis. As a result that the most important problem in the asymptotic expansion is the connections bound (coefficients bound), we introduce a study of this problem.

【 授权许可】

Unknown