38 citations · 70 across the 29 of their papers we have counts for
31 papers
Solution Space Characterisation of Perturbed Linear Volterra Integrodifferential Convolution Equations: the Lp case
John A. D. Appleby, Emmet Lawless
In this paper we characterise the Lp stability of perturbed linear Volterra integrodifferential convolution equations. Additionally we provide a framework which points to necessary…
Mean square asymptotic stability characterisation of perturbed linear stochastic functional differential equations
John Appleby, Emmet Lawless
In this paper we investigate the mean square asymptotic stability of a perturbed scalar linear stochastic functional differential equation. Specifically, we are able to give necess…
Blow-up and superexponential growth in superlinear Volterra equations
John A. D. Appleby, Denis D. Patterson
This paper concerns the finite-time blow-up and asymptotic behaviour of solutions to nonlinear Volterra integrodifferential equations. Our main contribution is to determine sharp e…
Growth Rates of Solutions of Superlinear Ordinary Differential Equations
John A. D. Appleby, Denis D. Patterson
In this letter we obtain sharp estimates on the growth rate of solutions to a nonlinear ODE with a nonautonomous forcing term. The equation is superlinear in the state variable and…
Growth and fluctuation in perturbed nonlinear Volterra equations
John A. D. Appleby, Denis D. Patterson
We develop precise bounds on the growth rates and fluctuation sizes of unbounded solutions of deterministic and stochastic nonlinear Volterra equations perturbed by external forces…
Hartman-Wintner growth results for sublinear functional differential equations
John A. D. Appleby, Denis D. Patterson
In this paper, we determine rates of growth to infinity of scalar autonomous nonlinear functional and Volterra differential equations. In these equations, the right-hand side is a…