Weak Topologies for Carathéodory Differential Equations: Continuous Dependence, Exponential Dichotomy and Attractors

Existence and continuous dependence for fractional neutral functional differential equations

In this paper, we investigate the existence, uniqueness and continuous dependence of solutions of fractional neutral functional differential equations with infinite delay and the Caputo fractional derivative order, by means of the Banach's contraction principle and the Schauder's fixed point theorem.

Attractors for Parametric Delay Differential Equations and their Continuous Behavior

The problem of the continuity of global attractors under minimal assumptions for a general class of parameterized delay differential equations is considered. The theory of equi-attraction developed by Li and Kloeden in [Li & Kloeden, 2004a] is adapted to this framework, so it is proved that the continuity of the attractors with respect to the parameter is equivalent to this equi-attraction prop...

Weak exponential schemes for stochastic differential equations with additive noise

This paper develops weak exponential schemes for the numerical solution of stochastic differential equations (SDEs) with additive noise. In particular, this work provides first and second-order methods which use at each iteration the product of the exponential of the Jacobian of the drift term with a vector. The article also addresses the rate of convergence of the new schemes. Moreover, numeri...

global results on some nonlinear partial differential equations for direct and inverse problems

در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...

On Exponential Dichotomy of Variational Difference Equations