4 papers · 1 filter
Critical perturbation sizes for preserving decay rates in solutions of perturbed nonlinear differential equations
John A. D. Appleby, Subham Pal
This paper develops necessary and sufficient conditions for the preservation of asymptotic convergence rates of deterministically and stochastically perturbed ordinary differential…
Characterisation of asymptotic behaviour of perturbed deterministic and stochastic pantograph equations
John A. D. Appleby, Emmet Lawless
This paper considers the asymptotic behaviour of deterministically and stochastically forced linear pantograph equations. The asymptotic behaviour is studied in the case when all s…
Solution space characterisation of perturbed linear functional and integrodifferential Volterra convolution equations: Cesà ro limits
John A. D. Appleby, Emmet Lawless
In this article we discuss the requirements needed in order to characterise the solution space of perturbed linear integro-differential Volterra convolution equations. We highlight…
Weighted Asymptotic Characterisation of Perturbed Autonomous Linear Ordinary and Stochastic Differential Equations: Part I -- ODEs
John A. D. Appleby, Emmet Lawless
This is the first of a two-part paper which determines necessary and sufficient conditions on the asymptotic behaviour of forcing functions so that the solutions of additively pert…