某些类型的非线性微分方程和微分差分方程解的存在性与不存在性
Existence and Nonexistence of Solutions of Certain type of Nonlinear Differential and Differential-Difference Equations
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中文总结 AI 辅助
本文利用Nevanlinna理论研究含fnf'项的非线性微分与差分方程，给出有限阶整函数解的不存在性结果，并完整刻画右侧为指数多项式的f2f'型方程的全部整函数解，改进并示例验证了已有结论。
中文摘要 AI 辅助
本文研究了涉及项fnf'的某些非线性微分方程和微分差分方程解的存在性、不存在性及增长行为。利用Nevanlinna理论中的工具，我们建立了涉及ff'的方程有限阶整函数解的几个不存在性结果。特别地，我们描述了右侧涉及指数多项式的f2f'类型的所有可能的整函数解。我们获得的结果改进了文献中已有的若干结果，并通过说明性例子进行了展示。
英文摘要
In this paper, we study the existence, nonexistence, and growth be haviour of solutions of certain nonlinear differential and differential-difference equa tions involving the term fnf'. Using tools from Nevanlinna theory, we establish several nonexistence results for finite-order entire solutions of equations involving ff'. In particular, we describe all the possible entire solutions of the type f2f' in which right hand side involves exponential polynomials. The results obtained by us improve several known results in the literature and we have them demonstrated through illustrative examples.
发表机构
- Department of Mathematics, University of Delhi（德里大学数学系）
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