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PreprintCC BY-NC-SA 4.0arXiv

Existence and Nonexistence of Solutions of Certain type of Nonlinear Differential and Differential-Difference Equations

  • Nidhi Gahlian
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Abstract

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.

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Cite

BibTeXRIS
BibTeX
@misc{gahlian2026existence,
  title = {{Existence and Nonexistence of Solutions of Certain type of Nonlinear Differential and Differential-Difference Equations}},
  author = {Nidhi Gahlian},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.29104},
  eprint = {2609.29104},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.29104},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - Existence and Nonexistence of Solutions of Certain type of Nonlinear Differential and Differential-Difference Equations
AU  - Nidhi Gahlian
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2609.29104
UR  - https://arxiv.org/abs/2609.29104
AB  - 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.
ER  -