Outputs (14)

Trajectories of a DAE near a pseudo-equilibrium (2004)
Journal Article
Beardmore, R. E., Laister, R., & Peplow, A. (2004). Trajectories of a DAE near a pseudo-equilibrium. Nonlinearity, 17(1), 253-279. https://doi.org/10.1088/0951-7715/17/1/015

We consider a class of differential-algebraic equations (DAEs) defined by analytic nonlinearities and study its singular solutions. The main assumption used is that the linearization of the DAE represents a Kronecker index-2 matrix pencil and that th... Read More about Trajectories of a DAE near a pseudo-equilibrium.

The flow of a DAE near a singular equilibrium (2003)
Journal Article
Beardmore, R. E., & Laister, R. (2003). The flow of a DAE near a singular equilibrium. SIAM Journal on Matrix Analysis and Applications, 24(1), 106-120. https://doi.org/10.1137/S0895479800378660

We extend the differential-algebraic equation (DAE) taxonomy by assuming that the linearization of a DAE about a singular equilibrium has a particular index-2 Kronecker normal form. A Lyapunov-Schmidt procedure is used to reduce the DAE to a quasilin... Read More about The flow of a DAE near a singular equilibrium.

Transversality and separation of zeros in second order differential equations (2003)
Journal Article
Laister, R., & Beardmore, R. E. (2003). Transversality and separation of zeros in second order differential equations. Proceedings of the American Mathematical Society, 131(1), 209-218. https://doi.org/10.1090/S0002-9939-02-06546-2

Sufficient conditions on the non-linearity f are given which ensure that non-trivial solutions of second order differential equations of the form Lu = f(t, u) have a finite number of transverse zeros in a given finite time interval. We also obtain a... Read More about Transversality and separation of zeros in second order differential equations.

Instability of equilibria in some delay reaction-diffusion systems (2000)
Journal Article
Laister, R. (2000). Instability of equilibria in some delay reaction-diffusion systems. Journal of Mathematical Analysis and Applications, 247(2), 588-607. https://doi.org/10.1006/jmaa.2000.6883

A new result is derived which extends a known instability result for a class of reaction-diffusion equations to a corresponding system incorporating time delay effects. For a significant class of nonlinear equations it is shown that an unstable equil... Read More about Instability of equilibria in some delay reaction-diffusion systems.