On Regularly Varying and History-Dependent Convergence Rates of Solutions of a Volterra Equation with Infinite Memory

Advances in Difference Equations

John A. D. Appleby¹ 

[1] Edgeworth Centre for Financial Mathematics, School of Mathematical Sciences, Dublin City University, Dublin 9, Ireland

关键词: Logistic Equation;    Volterra Equation;    Positive Continuous Function;    Volterra Operator;    Autocovariance Function;   

DOI  :  10.1155/2010/478291

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We consider the rate of convergence to equilibrium of Volterra integrodifferential equations with infinite memory. We show that if the kernel of Volterra operator is regularly varying at infinity, and the initial history is regularly varying at minus infinity, then the rate of convergence to the equilibrium is regularly varying at infinity, and the exact pointwise rate of convergence can be determined in terms of the rate of decay of the kernel and the rate of growth of the initial history. The result is considered both for a linear Volterra integrodifferential equation as well as for the delay logistic equation from population biology.

【 授权许可】

CC BY