Related papers: Asymptotic Behaviour of Nonlinear Evolution Equati…

We introduce a new concept of Yosida distance between two (unbounded) linear operators $A$ and $B$ in a Banach space $\mathbb{X}$ defined as $d_Y(A,B):=\limsup_{\mu\to +\infty} \| A_\mu-B_\mu\|$, where $A_\mu$ and $B_\mu$ are the Yosida…

It is shown how the linear method of the Yosida-approximation of the derivative applies to solve possibly nonlinear abstract functional differential equations in both, the finite and infinite delay case. A generalization of the integral…

In this paper we study the following non-autonomous stochastic evolution equation on a UMD Banach space $E$ with type 2, {equation}\label{eq:SEab}\tag{SE} {{aligned} dU(t) & = (A(t)U(t) + F(t,U(t))) dt + B(t,U(t)) dW_H(t), \quad t\in [0,T],…

In the underlying study it is shown how the linear method of the Yosida-approximation of the derivative applies to solve possibly nonlinear and multivalued functional differential equations like: \begin{eqnarray*} u^\prime(t) &\in&…

We consider some discrete and continuous dynamics in a Banach space involving a non expansive operator $J$ and a corresponding family of strictly contracting operators $\Phi(\lambda,x):=\lambda J(\frac{1-\lambda}{\lambda}x)$ for…

Stochastic evolution equations in Banach spaces with unbounded nonlinear drift and diffusion operators driven by a finite dimensional Brownian motion are considered. Under some regularity condition assumed for the solution, the rate of…

We examine a class of stochastic differential inclusions involving multiscale effects designed to solve a class of generalized variational inequalities. This class of problems contains constrained convex non-smooth optimization problems,…

The aim of this paper is to emphasize various concepts of dichotomies for evolution equations in Banach spaces, due to the important role they play in the approach of stable, instable and central manifolds. The asymptotic properties of the…

This paper considers a general framework for the study of the existence of quasi-variational and variational solutions to a class of nonlinear evolution systems in convex sets of Banach spaces describing constraints on a linear combination…

Sufficient conditions for the invariance of evolution problems governed by perturbations of (possibly nonlinear) $m$-accretive operators are provided. The conditions for the invariance with respect to sublevel sets of a constraint…

This paper is devoted to a comparison of early works of Kato and Yosida on the integration of non-autonomous linear evolution equations $\dot{x} = A(t)x$ in Banach space, where the domain $D$ of $A(t)$ is independent of $t$. Our focus is on…

We consider nonautonomous semilinear evolution equations of the form \label{semilineq} \frac{dx}{dt}= A(t)x+f(t,x). Here $A(t)$ is a (possibly unbounded) linear operator acting on a real or complex Banach space $\X$ and $f: \R\times\X\to\X$…

We study the asymptotic behavior of the trajectory of a nonautonomous evolution equation governed by a quasi-nonexpansive operator in Hilbert spaces. We prove the weak convergence of the trajectory to a fixed point of the operator by…

We study the existence of bounded asymptotic mild solutions to evolution equations of the form $u'(t)=Au(t)+f(t), t\ge 0$ in a Banach space $\X$, where $A$ generates an (analytic) $C_0$-semigroup and $f$ is bounded. We find spectral…

In an abstract Banach space we study conditions for the existence of piecewise continuous, almost periodic solutions for semi-linear impulsive differential equation with fixed and non-fixed moments of impulsive action

Known investigations of nonlinear evolution equations $${dx\over dt} + A(t)x(t) = f(t)\ ,\quad x(t_{0}) = x^{0},\ \quad t_{0} \le t < \infty\ , \eqno(0.1)$$ with monotone operators $A(t)$ acting from reflexive Banach space $B$ to dual space…

In this work, we prove the existence and uniqueness of $\mu$-pseudo almost automorphic solutions for some class of semilinear nonautonomous evolution equations of the form: $ u'(t)=A(t)u(t)+f(t,u(t)),\; t\in\mathbb{R} $ where $ (A(t))_{t\in…

Semilinear stochastic evolution equations with multiplicative L\'evy noise and monotone nonlinear drift are considered. Unlike other similar works, we do not impose coercivity conditions on coefficients. We establish the continuous…

In this paper, we generalize the classical Yosida approximation by utilizing a nonstandard duality mapping to establish the existence and uniqueness of both (probabilistically) weak and strong solutions and demonstrate the continuous…

We study the asymptotics of strongly continuous operator semigroups defined on locally convex spaces in order to develop a stability theory for solutions of evolution equations beyond Banach spaces. In the classical case, there is only…