PreprintCC BY-NC-SA 4.0arXiv
Meromorphic Solutions of Certain Kind of Non-Linear Differential equation with finite sums of Exponential Functions
Abstract
We study the existence and nonexistence of meromorphic solutions of nonlinear differential equations involving differential polynomials and finite sums of exponential-type functions with entire coefficients of controlled growth. Employ ing Nevanlinna theory, we obtain structural results showing that any admissible meromorphic solution must reduce to an exponential-type function governed by the dominant exponential term. The obtained lemma and main result strengthen several existing results in nonlinear complex differential equations with exponential terms.
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BibTeX
@misc{gahlian2026meromorphic,
title = {{Meromorphic Solutions of Certain Kind of Non-Linear Differential equation with finite sums of Exponential Functions}},
author = {Nidhi Gahlian and Sanjay Kumar},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29113},
eprint = {2609.29113},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29113},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Meromorphic Solutions of Certain Kind of Non-Linear Differential equation with finite sums of Exponential Functions
AU - Nidhi Gahlian
AU - Sanjay Kumar
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.29113
UR - https://arxiv.org/abs/2609.29113
AB - We study the existence and nonexistence of meromorphic solutions of nonlinear differential equations involving differential polynomials and finite sums of exponential-type functions with entire coefficients of controlled growth. Employ ing Nevanlinna theory, we obtain structural results showing that any admissible meromorphic solution must reduce to an exponential-type function governed by the dominant exponential term. The obtained lemma and main result strengthen several existing results in nonlinear complex differential equations with exponential terms.
ER -