Solutions for functional fully coupled forward–backward stochastic differential equations

Existence and multiplicity of positive solutions for a coupled system of perturbed nonlinear fractional differential equations

In this paper, we consider a coupled system of nonlinear fractional differential equations (FDEs), such that both equations have a particular perturbed terms. Using emph{Leray-Schauder} fixed point theorem, we investigate the existence and multiplicity of positive solutions for this system.

Mild Solutions of Neutral Stochastic Partial Functional Differential Equations

Existence and uniqueness of solutions of stochastic functional differential equations

We provide sufficient conditions on the coefficients of a stochastic functional differential equation with bounded memory driven by Brownian motion which guarantee existence and uniqueness of a maximal local and global strong solution for each initial condition. Our results extend those of previous works. For local existence and uniqueness, we only require the coefficients to be continuous and ...

Numerical Solutions of Neutral Stochastic Functional Differential Equations

This paper examines the numerical solutions of neutral stochastic functional differential equations (NSFDEs) d[x(t)− u(xt)] = f(xt)dt + g(xt)dw(t), t ≥ 0. The key contribution is to establish the strong mean square convergence theory of the Euler– Maruyama approximate solution under the local Lipschitz condition, the linear growth condition and the contractive mapping. These conditions are gene...

Explosive and non - explosive solutions of stochastic functional differential equations

The paper covers questions relating to the existence, explosion, and prevention of explosion, of solutions of stochastic functional differential equations (SFDEs) of Itô type. It is well-known that solutions of a deterministic ordinary differential equation x(t) = f(x(t)) can explode in finite time if the function f does not obey a global linear bound; however, uniqueness up to the explosion ti...