On the transcendental entire and meromorphic solutions of certain non-linear generalized delay-differential equations

A. Banerjee, T. Biswas
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Abstract

Abstract The prime intention of this paper is to study the conditions under which certain non-linear generalized delay-differential equations possess a solution. In this respect, by extending and improving recent results of [5, 15], we characterize the nature of solutions. By providing relevant examples in a remark, we also show that for the uniqueness of solutions the conditions on the Borel exceptional value can not be removed. Finally, to determine explicitly all forms of the solutions of a traditional generalized delay-differential equation, we deal with the situation under the aegis of generalized c-delay-differential equations. We exhibit some examples to show that the conclusions of the theorems actually occur.
一类非线性广义时滞微分方程的超越全解和亚纯解
摘要本文的主要目的是研究一类非线性广义时滞微分方程具有解的条件。在这方面,通过扩展和改进[5,15]的最新结果,我们描述了解的性质。通过在评论中提供相关的例子,我们也证明了对于解的唯一性,Borel异常值的条件是不能去除的。最后,为了显式确定传统广义时滞微分方程解的所有形式,我们在广义c-时滞微分方程的支持下处理了这种情况。我们举出一些例子来证明这些定理的结论实际上是成立的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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