Entire solutions of a class of algebraic Briot–Bouquet differential equations utilizing majority concept

Advances in Difference Equations

article

Ibrahim, Rabha W.¹  Baleanu, Dumitru³ 

[1] Informetrics Research Group, Ton Duc Thang University;Faculty of Mathematics & Statistics, Ton Duc Thang University;Department of Mathematics, Cankaya University;Institute of Space Sciences;Department of Medical Research, China Medical University

关键词: Analytic function;    Subordination;    Univalent function;    Open unit disk;    Algebraic differential equations;    Majorization method;   

DOI  :  10.1186/s13662-020-03138-2

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In this effort, the analytic solution of a class of algebraic Briot–Bouquet differential equations (ABBDE) in the open unit disk is investigated by making use of a major theory. The class is presented by the formula$$\begin{aligned}& \alpha _{1}\varphi ^{\prime 3}(z) + \alpha _{2} \varphi ^{ ' 2} (z) \varphi (z) + \alpha _{3} \varphi ^{\prime } (z) \varphi ^{2} (z) +\aleph ^{k}_{\varphi }(z) = 0, \\& \aleph ^{k}_{\varphi }(z):= a_{k} \varphi ^{k}(z)+a_{k-1} \varphi ^{k-1}(z)+\cdots+ a_{1} \varphi (z)+ a_{0}. \end{aligned}$$The conformal analysis (angle-preserving) of the ABBDEs is considered. Analytic outcomes of the ABBDEs are indicated by employing the major method. Some special cases are investigated.

【 授权许可】

CC BY