We consider a certain type of second-order neutral delay differential systems and we
establish two results concerning the oscillation of solutions after the system undergoes …

We study the dynamics of relativistic shear-free gravitating fluids in higher dimensions for
both neutral and charged matter. We reduce the Einstein–Maxwell equations to a single …

The derivation of conservation laws and invariant functions is an essential procedure for the
investigation of nonlinear dynamical systems. In this study, we consider a two-field …

This is an important and natural question as the spacetime shear, inhomogeneity and tidal
effects are all intertwined via the Einstein field equations. Though many solutions with these …

Abstract The Emden-Fowler equation of index n is studied utilising the techniques of Lie and
Painlevé analysis. For general n information about the integrability of this equation is …

We study the underlying nonlinear partial differential equation that governs the behaviour of
spherically symmetric charged fluids in general relativity. We investigate the conditions for …

The integrability properties of the field equation L xx= F (x) L 2 of a spherically symmetric
shear-free fluid are investigated. A first integral, subject to an integrability condition on F (x) …

The McVittie metric is found to suffer inherent limitations. It is shown that the radius of the
metric associated to the sphere has a correct asymptotic behaviour, à la Schwarzschild at …

A single master equation governs the behaviour of shear-free neutral perfect fluid
distributions arising in gravity theories. In this paper, we study the integrability of yxx= f (x) y …

We consider the time-dependent dynamical system q¨ a=− Γ bcaq˙ bq˙ c− ω (t) Q a (q) where
ω (t) is a non-zero arbitrary function and the connection coefficients Γ bca are computed from …