29 citations · 73 across the 14 of their papers we have counts for
8 papers · 1 filter
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…
Memory Dependent Growth in Sublinear Volterra Differential Equations
John A. D. Appleby, Denis D. Patterson
We investigate memory dependent asymptotic growth in scalar Volterra equations with sublinear nonlinearity. To obtain precise results we utilise the powerful theory of regular vari…
Growth Rates of Sublinear Functional and Volterra Differential Equations
John A. D. Appleby, Denis D. Patterson
This paper considers the growth rates of positive solutions of scalar nonlinear functional and Volterra differential equations. The equations are assumed to be autonomous (or asymp…
Subexponential Growth Rates in Functional Differential Equations
John A. D. Appleby, Denis D. Patterson
This paper determines the rate of growth to infinity of a scalar autonomous nonlinear functional differential equation with finite delay, where the right hand side is a positive co…
On Necessary and Sufficient Conditions for Preserving Convergence Rates to Equilibrium in Deterministically and Stochastically Perturbed Differential Equations with Regularly Varying Nonlinearity
John A. D. Appleby, Denis D. Patterson
This paper develops necessary and sufficient conditions for the preservation of asymptotic convergence rates of deterministically and stochastically perturbed ordinary differential…