Stability properties of solutions of linear Volterra integro-differential equations

Positive Solutions of Volterra Integro–differential Equations

We present some sufficient conditions such that Eq. (1) only has solutions with zero points in (0,∞). Moreover, we also obtain some conditions such that Eq. (1) has a positive solution on [0,+∞). The motivation of this work comes from the work of Ladas, Philos and Sficas [5]. They discussed the oscillation behavior of Eq. (1) when P (t, s) = P (t− s) and g(t) = t. They obtained a necessary and ...

Numerical Solutions of Special Class of Systems of Non-Linear Volterra Integro-Differential Equations by a Simple High Accuracy Method

Stability of a system of Volterra integro-differential equations

Using new and known forms of Lyapunov functionals, this paper proposes new stability criteria for a system of Volterra integro-differential equations.  2003 Elsevier Science (USA). All rights reserved.

Blow-up solutions of nonlinear Volterra integro-differential equations

The paper studies the finite-time blow-up theory for a class of nonlinear Volterra integro-differential equations. The conditions for the occurrence of finite-time blow-up for nonlinear Volterra integro-differential equations are provided. Moreover, the finite-time blow-up theory for nonlinear partial Volterra integro-differential equations with general kernels is also established using the blo...

Stochastic Volterra integro-differential equations: stability and numerical methods

We consider the reliability of some numerical methods in preserving the stability properties of the linear stochastic functional differential equation ẋ(t) = αx(t) + β ∫ t 0 x(s)ds+ σx(t− τ )Ẇ (t), where α, β, σ, τ ≥ 0 are real constants, and W (t) is a standard Wiener process. We adopt the shorthand notation of ẋ(t) to represent the differential dx(t) etc. Our choice of test equation is a stoc...