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In this paper, we study the existence and non-existence of entire solutions of certain non-linear delay-differential equations.

Complex Variables · Mathematics 2024-07-30 Nidhi Gahlian

In this paper we study about the existence of solutions of certain kind of non-linear differential and differential-difference equations. We give partial answer to a problem which was asked by chen et al. in [13].

Complex Variables · Mathematics 2022-02-09 Garima Pant , Manisha Saini

In this paper, we have considered second order non-homogeneous linear differential equations having entire coefficients. We have established conditions ensuring non-existence of finite order solution of such type of differential equations.

Complex Variables · Mathematics 2021-03-24 Dinesh Kumar , Sanjay Kumar , Manisha Saini

In this paper, we study the transcendental entire solutions for the nonlinear differential-difference equations of the forms: $f^{2}(z)+\widetilde{\omega} f(z)f'(z)+q(z)e^{Q(z)}f(z+c)=u(z)e^{v(z)}$, and $f^{n}(z)+\omega…

Complex Variables · Mathematics 2021-02-05 Nan Li , Jiachuan Geng , Lianzhong Yang

This article deals with the second order linear differential equations with entire coefficients. We prove some results involving conditions on coefficients so that the order of growth of every non-trivial solution is infinite.

Complex Variables · Mathematics 2021-02-24 Garima Pant , Manisha Saini

In this paper we establish some results about the existence and precise forms of finite order entire solutions of some systems of quadratic trinomial functional equations one of which in $\mathbb{C}^n$, $n\in\mathbb{N}$ and other two in…

Complex Variables · Mathematics 2023-11-02 Goutam Haldar

We show that the higher order linear differential equation possesses all solutions of infinite order under certain conditions by extending the work of authors about second order differential equation \cite{dsm2}.

Complex Variables · Mathematics 2020-04-10 Dinesh Kumar , Sanjay Kumar , Manisha Saini

In this paper, we mainly investigate on the finite order transcendental entire solutions of two Fermat types delay-differential and one Fermat type c-shift equations, as these types were not considered earlier. Our results improve those of…

Complex Variables · Mathematics 2021-05-06 Abhijit Banerjee , Tania Biswas

There is no general existence theorem for solutions for nonlinear difference equations, so we must prove the existence of solutions in accordance with models one by one. In our work, we found theorems for the existence of analytic solutions…

Classical Analysis and ODEs · Mathematics 2007-05-23 Mami Suzuki

Using Nevanlinna's value distribution theory and the complex difference theory , the existence of the finite order of the entire solutions of the Fermat type of the complex differential-difference equation and the systems of complex…

Complex Variables · Mathematics 2017-12-25 Xianfeng Su , Qingcai Zhang

In this paper, we study all possible orders which are less than 1 of transcendental entire solutions of linear difference equations \begin{equation} P_m(z)\Delta^mf(z)+\cdots+P_1(z)\Delta f(z)+P_0(z)f(z)=0,\tag{+} \end{equation} where…

Complex Variables · Mathematics 2023-01-18 Katsuya Ishizaki , Zhi-Tao Wen

For a second order linear differential equation $f''+A(z)f'+B(z)f=0$, with $ A(z)$ and $B(z)$ being transcendental entire functions under some restriction, we have established that all non-trivial solutions are of infinite order. In…

Complex Variables · Mathematics 2020-07-29 Manisha Saini , Sanjay Kumar

In this paper, we study the existence and uniqueness of periodic solutions of the differential equation of the form . Here, we obtain some sufficient conditions which guarantee the existence of periodic solutions. This equation is a quite…

Classical Analysis and ODEs · Mathematics 2011-08-23 Muzaffer Ates

This article is devoted to the study of solutions of non-homogenous linear differential equations having entire coefficients. We get all non-trivial solutions of infinite order of equation $f^{(n)}+a_{n-1}(z)f^{(n-1)}+\ldots…

Complex Variables · Mathematics 2022-08-24 Naveen Mehra , S. K. Chanyal

The existence of sufficiently many finite order meromorphic solutions of a differential equation, or difference equation, or differential-difference equation, appears to be a good indicator of integrability. In this paper, we investigate…

Classical Analysis and ODEs · Mathematics 2018-08-14 Li-Hao Wu , Ran-Ran Zhang , Zhi-Bo Huang

The objective of this paper is to investigate the existence and the forms of the pair of finite order entire and meromorphic solutions of some certain systems of Fermat-type partial differential-difference equations of several complex…

Complex Variables · Mathematics 2026-04-14 Raju Biswas , Rajib Mandal

In this paper, we study the growth of transcendental entire solutions of linear difference equations \begin{equation} P_m(z)\Delta^mf(z)+\cdots+P_1(z)\Delta f(z)+P_0(z)f(z)=0,\tag{+} \end{equation} where $P_j(z)$ are polynomials for…

Complex Variables · Mathematics 2025-04-04 Xiong-Feng Liu , Zhi-Tao Wen , Can-Xin Zhu

In this paper we mainly study the existence and the form of entire solutions with finite order for the following system of Fermat-type difference and partial differential-difference equations $$\begin{cases} f_1(z)^2+(\Delta_cf_2(z))^2=1\cr…

Complex Variables · Mathematics 2022-01-27 Goutam Haldar

The aim of this study is to investigate the precise form of finite-order entire solutions to the following system of Fermat-type partial differential-difference equations: \beas \begin{cases} \left(\frac{\partial f_1\left(z_1, z_2, \ldots,…

Complex Variables · Mathematics 2025-12-03 Junfeng Xu , Sujoy Majumder , Debabrata Pramanik

This paper is mainly devoted to describing the entire solutions of nonlinear partial differential equation $$ u_{z_1}u_{z_2}\cdots u_{z_n}=e^g, $$ with the eikonal equation as a prototype, where $g$ is a polynomial in $\mathbb{C}^n$.…

Complex Variables · Mathematics 2026-05-12 Feng Lü
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