Manisha Saini

• Researcher at University of Delhi

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].

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.

We show that all non-trivial solutions of complex differential equation \(f''+ A(z)f'+B(z)f = 0\) are of infinite order if coefficients A(z) and B(z) are of special type and establish a relation between the hyper-order of these solutions and the orders of coefficients A(z) and B(z). We have also extended these results to higher order complex differ...

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}.

In this paper, we will prove that all non-trivial solutions of $f''+A(z)f'+B(z)f=0$ are of infinite order, where we have some restrictions on entire functions $A(z)$ and $B(z)$.

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.

In this paper, we establish transcendental entire function A(z) and polynomial B(z) such that the differential equation f +A(z)f +B(z)f = 0, has all non-trivial solution of infinite order. We use the notion of critical rays of the function e P (z) , where A(z) = d(z)e P (z) with some restrictions.

We have disscussed the problem of finding the condition on coefficients of f + A(z)f + B(z)f = 0, B(z) ≡ 0 so that all non-trivial solutions are of infinite order. The hyper-order of non-trivial solution of infinite order is found when λ(A) < ρ(B) and ρ(B) = ρ(A) or B(z) has Fabry gap.

It is an expanded form of Drasin's work on normality of family of meromorphic functions given in his seminal paper titled "Normal Families and the Nevanlinna Theory".

In this paper, we establish transcendental entire function A(z) and polynomial B(z) such that the differential equation f ′′ + A(z)f ′ + B(z)f = 0, has all non-trivial solution of infinite order. We use the notion of critical rays of the function e P (z) , where A(z) = d(z)e P (z) with some restrictions.

In this paper, we establish transcendental entire function $A(z)$ and polynomial $B(z)$ such that the differential equation $f''+A(z)f'+B(z)f=0$, has all non-trivial solution of infinite order. We use the notion of \emph{critical rays} of the function $e^{P(z)}$, where $A(z)=d(z)e^{P(z)}$ with some restrictions.

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 addition, we have proved that these solutions have infinite number of zeros. Also, we have extended these results to...

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 addition, we have proved that these solutions have infinite number of zeros.