Asymptotic stability of solutions to Volterra-renewal integral equations with space maps

Exact solutions of nonlinear interval Volterra integral equations

Solutions for Singular Volterra Integral Equations

0 gi(t, s)[Pi(s, u1(s), u2(s), · · · , un(s)) + Qi(s, u1(s), u2(s), · · · , un(s))]ds, t ∈ [0, T ], 1 ≤ i ≤ n where T > 0 is fixed and the nonlinearities Pi(t, u1, u2, · · · , un) can be singular at t = 0 and uj = 0 where j ∈ {1, 2, · · · , n}. Criteria are offered for the existence of fixed-sign solutions (u∗1, u ∗ 2, · · · , u ∗ n) to the system of Volterra integral equations, i.e., θiu ∗ i (...

Asymptotic Behavior of Solutions of Discrete Volterra Equations

f : N × R → R, K : N × N → R, K(n, i) = 0 for n < i, and b : N → R. We regard N× R as a metric subspace of the Euclidean plane R2. By a solution of (E) we mean a sequence x : N→ R satisfying (E) for all large n. We say that x is a full solution of (E) if (E) is satisfied for all n. Moreover, if p ∈ N and (E) is satisfied for all n ≥ p, then we say that x is a p-solution. For the sake of conveni...

Asymptotic Stability Results for Certain Integral Equations

This paper shows the existence of asymptotically stable solutions to an integral equation. This is done by using a fixed point theorem, and without requiring that the solutions be bounded.

Asymptotic Representation of the Solutions of Linear Volterra Difference Equations

This article analyses the asymptotic behaviour of solutions of linear Volterra difference equations. Some sufficient conditions are presented under which the solutions to a general linear equation converge to limits, which are given by a limit formula. This result is then used to obtain the exact asymptotic representation of the solutions of a class of convolution scalar difference equations, w...