We study stochastic perturbed Volterra equations of convolution type in an infinite dimensional case. Our interest is directed towards the existence and regularity of stochastic convolutions connected to the equations considered under some kind of perturbations. We use an operator theoretical method for the representation of solutions.

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We construct a class of linear Lyapunov functions for Volterra quadratic stochastic operator. Using these functions we improve known results about ω-limit set of trajectories of the Volterra quadratic operators.

This paper presents (1) a brief overview of several concepts important to predator-prey behaviors of coyotes, (2) results of an enclosure study of sheep-attack, -immobilization, and -ingestion responses involving 12 male coyotes (Canis latrans) that were paired with sheep after observing various sheeppredation events by conspecifics, and (3) an analysis of sheep predation based upon operant lea...

In this article, we have studied the difference-difference Lotka-Volterra equations in p-adic number space and its p-adic valuation version. We pointed out that the structure of the space given by taking the ultra-discrete limit is the same as that of the p-adic valuation space.

In this letter, the numerical scheme of nonlinear Volterra-Fredholm integro-differential equations is proposed in a reproducing kernel Hilbert space (RKHS). The method is constructed based on the reproducing kernel properties in which the initial condition of the problem is satised. The nonlinear terms are replaced by its Taylor series. In this technique, the nonlinear Volterra-Fredholm integro...

In this study, a new application of Taylor expansion is considered to estimate the solution of Volterra-Fredholm integral equations (VFIEs) and systems of Volterra-Fredholm integral equations (SVFIEs). Our proposed method is based upon utilizing the nth-order Taylor polynomial of unknown function at an arbitrary point and employing integration method to convert VFIEs into a system of linear equ...

We obtain boundness and asymptotic behavior of solutions for semilinear functional difference equations with infinite delay. Applications on Volterra difference equations with infinite delay are shown.

In this paper, the two-dimensional triangular orthogonal functions (2D-TFs) are applied for solving a class of nonlinear two-dimensional Volterra integral equations. 2D-TFs method transforms these integral equations into a system of linear algebraic equations. The high accuracy of this method is verified through a numerical example and comparison of the results with the other numerical methods.