Weak generalized solutions of abstract differential equations

On Periodic Solutions of Abstract Differential Equations

Asymptotic Stability of Solutions to Abstract Differential Equations

An evolution problem for abstract differential equations is studied. The typical problem is: u̇ = A(t)u+F(t,u), t ≥ 0; u(0) = u0; u̇ = du dt (∗) Here A(t) is a linear bounded operator in a Hilbert spaceH, and F is a nonlinear operator, ‖F(t,u)‖≤ c0‖u‖, p > 1, c0, p = const > 0. It is assumed that Re(A(t)u,u) ≤ −γ(t)‖u‖2 ∀u ∈ H, where γ(t) > 0, and the case when limt→∞ γ(t) = 0 is also considered....

Almost Automorphic Solutions to Abstract Fractional Differential Equations

Copyright q 2010 Hui-Sheng Ding et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. A new and general existence and uniqueness theorem of almost automorphic solutions is obtained for the semilinear fractional differential equat...

Global solutions for impulsive abstract partial differential equations

In this paper, we study the existence of global solutions for a class of impulsive abstract functional differential equation. An application involving a parabolic system with impulses is considered. c © 2008 Elsevier Ltd. All rights reserved.

Strong solutions for differential equations in abstract spaces

Let (E,F) be a locally convex space. We denote the bounded elements of E by Eb : ={x ∈ E : ‖x‖F = sup ∈F (x)<∞}. In this paper, we prove that if BEb is relatively compact with respect to the F topology and f : I × Eb → Eb is a measurable family of F-continuous maps then for each x0 ∈ Eb there exists a norm-differentiable, (i.e. differentiable with respect to the ‖ · ‖F norm) local solution to t...