arXiv subjects

Lata Mahato

Publications and source records attributed to Lata Mahato.

3 recordsLinked to original sources

arXiv2025

Relationship between the value-sharing behavior of an entire function and its derivative, and the analytic structure of a nonlinear differential equation

In this paper, we study uniqueness problems for entire functions that partially share two values with their higher-order derivatives. The results obtained here both improve and generalize the related results of Li and Yi \cite{LYi}, L\"{u} et al. \cite{LXY1} and Sauer and Schweizer \cite{SS1}. Furthermore, we show that our results reveal a deep relationship between the value-sharing behavior of an entire function $f$ and its $k$-th derivative $f^{(k)}$, and the analytic structure of a particular type of nonlinear differential equation. Several examples are provided to illustrate the necessity of the conditions used in our results.

math.CV↗

arXiv2025

On the two conjectures

In this paper, we investigate the uniqueness problem of entire functions that share an entire function with their higher-order difference operators. We obtain two results that confirm the conjectures posed by Liu and Laine \cite{LL1} and by Zhang et al. \cite{ZKL1}, respectively. In addition, we present several relevant examples to further illustrate and support our findings

math.CV↗

arXiv2025

Meromorphic solution of a certain type of algebraic differential equation

In the paper, we use the idea of normal family to find out the possible solution of the following special case of algebraic differential equation \[P_k\big(z,f,f^{(1)},\ldots, f^{(k)}\big)=f^{(1)}(f-\mathscr{L}_k(f))-\varphi (f-a)(f-b)=0,\] where $\mathscr{L}_k(f)=\sideset{}{_{i=0}^k}{\sum} a_i f^{(i)}$ and $\varphi$ is an entire function, $a_i\in\mathbb{C}\;(i=0,1,\ldots, k)$ such that $a_k=1$ and $a, b\in\mathbb{C}$ such that $a\neq b$. The obtained results improve and generalise the results of Li and Yang \cite{LY1} and Xu et al. \cite{XMD} in a large scale.

math.CV↗