Conditions are given for a class of nonlinear ordinary differential equations x′′ + a(t)w(x) = 0, t ≥ t0 ≥ 1, which includes the linear equation to possess solutions x(t) with prescribed oblique asymptote that have an oscillatory pseudo-wronskian x′(t)− x(t) t .

We discuss the solution of a nonlinear ordinary differential equation that appears in a model for MHD viscous flow caused by a shrinking sheet. We propose an accurate numerical solution and derive simple analytical expressions. Our results suggest that a recent perturbation treatment of the same problem exhibits a pathological behaviour and conjecture its probable cause.

The steady heat transfer through a rectangular longitudinal fin is studied.The thermal conductivity and heat transfer coefficient are assumed to be temperature dependent making the resulting ordinary differential equation (ODE) highly nonlinear. An asymptotic solution is used as a means of understanding the relationship between key parameters. A dynamical analysis is also employed for the same ...

The repeated homogeneous balance method is used to construct new exact traveling wave solutions of the (2+1) dimensional ZakharovKuznetsov (ZK) equation, in which the homogeneous balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation, respectively. Many new exact traveling wave solutions are successfully obtained. This method is straight...

Let G and f : [0,1]×R4 → R be two functions satisfying Caratheodory conditions. This paper is concerned with the problems of existence and uniqueness of solutions for the nonlinear fourth-order ordinary differential equation y′′′′ +λy′′ +ky+G(x,y,y′,y′′,y′′′)= f (x,y,y′,y′′,y′′′) with one of a particular set of boundary conditions.

In this article, we discuss the existence as well as global attractivity and ultimate positivity of solutions for a certain nonlinear first order ordinary differential equation on the unbounded intervals of real line via a classical fixed point theorem of Schauder (Smart [12, page 15]). Our hypotheses and claims have also been explained with the help of two realizations under some natural condi...

Similarity reductions of the coupled nonlinear Schrödinger equation and an integrable version of the coupled Maxwell-Bloch system are obtained by applying non-translational symmetries. The reduced system of coupled ordinary differential equations are solved in terms of Painlevé transcendents, leading to new exact self-similar solutions for these integrable equations. PACS numbers: 02.30.Ik., 02...

In this paper we consider the pair diffusion process in more than two spatial dimensions. In this case we are able to prove just a local existence result, since it is not possible to deduce global a priori estimates for the equations as it can be done in the two-dimensional case. The model includes a nonlinear system of reaction-drift-diffusion equations, a nonlinear ordinary differential equat...