Results 31 to 40 of about 123 (69)

Existence, uniqueness, and regularity of solutions to semilinear retarded differential equations

International Journal of Stochastic Analysis, Volume 2004, Issue 3, Page 213-219, 2004., 2004
In the present work, we consider a semilinear retarded differential equation in a Banach space. We first establish the existence and uniqueness of a mild solution and then prove its regularity under different additional conditions. Finally, we consider some applications of the abstract results.
D. Bahuguna
wiley   +1 more source

A Massera‐type criterion for almost periodic solutions of higher‐order delay or advance abstract functional differential equations

Abstract and Applied Analysis, Volume 2004, Issue 10, Page 881-896, 2004., 2004
Let u be a given bounded uniformly continuous mild solution of a higher‐order abstract functional differential equation of delay or advance type. We give a so‐called Massera‐type criterion for the existence of a mild solution, which is a “spectral component” of u with spectrum similar to the one of the forcing term f.
Nguyen Van Minh, Ha Binh Minh
wiley   +1 more source

The Kneser property for abstract retarded functional differential equations with infinite delay

International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 26, Page 1645-1661, 2003., 2003
We establish existence of mild solutions for a class of semilinear first‐order abstract retarded functional differential equations (ARFDEs) with infinite delay and we prove that the set consisting of mild solutions for this problem is connected in the space of continuous functions.
Hernán R. Henríquez
wiley   +1 more source

About reducing integro-differential equations with infinite limits of integration to systems of ordinary differential equations

Advances in Differential Equations, 2013
The purpose of this paper is to propose a method for studying integro-differential equations with infinite limits of integration. The main idea of this method is to reduce integro-differential equations to auxiliary systems of ordinary differential ...
Y. Goltser, A. Domoshnitsky
semanticscholar   +2 more sources

Monotone iterative technique for non-autonomous semilinear differential equations with nonlocal condition

Demonstratio Mathematica, 2019
The objective of this article is to discuss the existence and uniqueness of mild solutions for a class of non-autonomous semilinear differential equations with nonlocal condition via monotone iterative method with upper and lower solutions in an ordered ...
Meraj Arshi, Pandey Dwijendra Narain
doaj   +1 more source

Linear neutral partial differential equations: a semigroup approach

International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 23, Page 1433-1445, 2003., 2003
We study linear neutral PDEs of the form (∂/∂t)Fut = BFut + Φut, t ≥ 0; u0(t) = φ(t), t ≤ 0, where the function u(⋅) takes values in a Banach space X. Under appropriate conditions on the difference operator F and the delay operator Φ, we construct a C0‐semigroup on C0(ℝ−, X) yielding the solutions of the equation.
Rainer Nagel, Nguyen Thieu Huy
wiley   +1 more source

EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR SOME NEUTRAL DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAYS

, 2018
In this work, we establish several results about the existence and uniqueness of solutions for some neutral differential equations with state-dependent delays.
K. Daoudi, J. Henderson, A. Ouahab
semanticscholar   +1 more source

Functional integro‐differential stochastic evolution equations in Hilbert space

International Journal of Stochastic Analysis, Volume 16, Issue 2, Page 141-161, 2003., 2003
We investigate a class of abstract functional integro‐differential stochastic evolution equations in a real separable Hilbert space. Global existence results concerning mild and periodic solutions are formulated under various growth and compactness conditions.
David N. Keck, Mark A. McKibben
wiley   +1 more source

Existence of solutions for nonlinear mixed type integro-differential functional evolution equations with nonlocal conditions

Boundary Value Problems, 2012
Using the Mönch fixed point theorem, this article proves the existence of mild solutions for nonlinear mixed type integro-differential functional evolution equations with nonlocal conditions in Banach spaces.
S. Xie
semanticscholar   +2 more sources

A class of linear dynamical equations for a Banach space on time scales

Advances in Differential Equations, 2013
In this paper we consider the existence and uniqueness of global solutions to linear dynamical equations for a Banach space on time scales from a new point of view.
Youling Feng
semanticscholar   +2 more sources