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Nidhi Gahlian

Publications and source records attributed to Nidhi Gahlian.

6 recordsLinked to original sources
arXiv2026

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

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.

math.CV↗
arXiv2026

Meromorphic Solutions of Certain Kind of Non-Linear Differential equation with finite sums of Exponential Functions

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.

math.CV↗
arXiv2026

Study of solutions of certain type of non-linear differential-difference equations

In this paper, we analyze the solutions of the following non-linear differential-difference equations f^n(z) +ωf^(n-1)f'(z) +p(z)f(z+c) = p_1e^α_1z +p_2e^α_2z and f^n(z)f'(z) +q(z)e^Q(z)f(z+c) = p_1e^α_1z +p_2e^α_2z, where n is a positive integer,ω, p1, p2,α1 & α2 are non-zero constants satisfying α1 not equal to α2, α1/α2 not equal to (n)^+-1, q(z) is a non-vanishing polynomial and Q(z) is a non-constant polynomial.

math.CV↗
arXiv2023

Oscillation results of higher order linear differential equation

We study higher order linear differential equation $y^{(k)}+A_1(z)y=0$ with $k\geq2$, where $A_1=A+h$, $A$ is a transcendental entire function of finite order with $\frac{1}{2}\leq μ(A)<1$ and $h\neq0$ is an entire function with $ρ(h)<μ(A)$. Then it is shown that, if $f^{(k)}+A(z)f=0$ has a solution $f$ with $λ(f)<μ(A)$ then exponent of convergence of zeros of any non trivial solutions of $y^{(k)}+A_1(z)y=0$ is infinite.

math.CV↗
arXiv2022

On Hayman Conjecture for Paired Complex Delay-Differential Polynomials

We study Hayman conjecture for different paired complex polynomials under certain conditions. In 2021, the zeros distribution of $f^{n}(z)L(g)-a(z)$ and $g^{n}(z)L(f)-a(z)$ was studied by Gao and Liu for $n\geq 3$. In this paper, we work on the zeros distribution of $f^{2}(z)L(g)-a(z)$ and $g^{2}(z)L(f)-a(z)$, where $a(z)$ is a non-zero small function of both $f(z)$ and $g(z)$, and $L(h)$ takes the $k$th derivative $h^{(k)}(z)$ or shift $h(z+c)$ or difference $h(z+c)-h(z)$ or delay-difference $h^{(k)}(z+c)$, here $k\geq 1$ and $c$ is a non-zero constant. Moreover, we discuss Hayman conjecture for paired complex differential polynomials when $n=1.$

math.CV↗