38 citations · 70 across the 29 of their papers we have counts for
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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…
Large fluctuations and growth rates of linear Volterra summation equations
John A. D. Appleby, Denis D. Patterson
This paper concerns the asymptotic behaviour of solutions of a linear convolution Volterra summation equation with an unbounded forcing term. In particular, we suppose the kernel i…
On the admissibility of unboundedness properties of forced deterministic and stochastic sublinear Volterra summation equations
John A. D. Appleby, Denis D. Patterson
In this paper we consider unbounded solutions of perturbed convolution Volterra summation equations. The equations studied are asymptotically sublinear, in the sense that the state…
Exact and memory--dependent decay rates to the non--hyperbolic equilibrium of differential equations with unbounded delay and maximum functional
John A. D. Appleby
In this paper, we obtain the exact rates of decay to the non--hyperbolic equilibrium of the solution of a functional differential equation with maxima and unbounded delay. We study…
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…