Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2609.29104

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

Nidhi Gahlian
View original source ↗Read source document ↗Export metadata ↓

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.

Explore related subjects

math.CV

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Nidhi Gahlian. 2026-09-24. Existence and Nonexistence of Solutions of Certain type of Nonlinear Differential and Differential-Difference Equations. https://arxiv.org/abs/2609.29104

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Hilbert metric and quasiconformal mappings

We prove a functional identity between the Hilbert metric and the visual angle metric in the unit disk. The proof utilizes the Poincaré hyperbolic metric in terms of which both metrics can be expressed. This identity then yields sharp distortion results for quasiregular mappings and analytic functions, expressed in terms of the Hilbert metric. We also prove that Hilbert circles are, in fact, Euclidean ellipses. The proof makes use of computer algebra methods. In particular, Gröbner bases are used.

math.CV↗
arXiv2026

Cyclicity in Poletsky-Stessin Weighted Bergman Spaces

We study the cyclicity of polynomials in Poletsky-Stessin weighted Bergman spaces on various domains in $\mathbb{C}^2$, including the unit ball, the bidisk, and the complex ellipsoid. To this end, we introduce a natural extension of the parameter range for Poletsky-Stessin weighted Bergman spaces on complete Reinhardt domains, yielding a family of spaces that resemble Dirichlet-type spaces on the unit ball. We highlight the differences in the cyclicity behavior of polynomials in these spaces on the bidisk compared to those studied by Bénéteau et al. Finally, we propose several open problems concerning the structure of cyclic polynomials in these spaces.

math.CV↗
arXiv2026

Schwarz-contractivity of the Poisson operator

We say that the Poisson operator $P_r$ is Schwarz-contractive from a space $X$ to a space $Y$ if $\|P_r\|_{X\to Y}\le r$ holds for all $0<r<1$. The classical Schwarz lemma is the case $H^\infty_0\to H^\infty$, the subscript indicating zero mean. We are concerned with the non-holomorphic case $L^\infty_0 \to L^p$. For real functions Schwarz-contractivity holds up to the sharp exponent $p_{\mathbb R}=4.109\ldots$. For complex functions we prove it for $p\le 3$ and conjecture that the critical exponent is $4$.

math.CV↗