Related papers: Monotone iterative technique for delayed evolution…

In the present work we give some sufficient conditions to obtain a unique almost automorphic solution to abstract nonlinear integral equations which are simultaneously of advanced and delayed type and also a unique asymptotically almost…

Stochastic partial differential equations (SPDEs) have become a key modelling tool in applications. Yet, there are many classes of SPDEs, where the existence and regularity theory for solutions is not completely developed. Here we…

We prove the existence of a weak solution for a general class of Dirichlet anisotropic elliptic problems such as $\mathcal Au+\Phi(x,u,\nabla u)=\mathfrak{B}u+f$ in $\Omega$, where $\Omega$ is a bounded open subset of $\mathbb R^N$ and…

We consider the following quasi-linear parabolic system of backward partial differential equations on a Banach space $E$: $(\partial_t+L)u+f(\cdot,\cdot,u, A^{1/2}\nabla u)=0$ on $[0,T]\times E,\qquad u_T=\phi$, where $L$ is a possibly…

This paper investigates the dynamical behavior of periodic solutions for a class of second-order non-autonomous differential equations. First, based on the Lyapunov-Schmidt reduction method for finite-dimensional functions, the…

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 addresses the existence of nonnegative mild solutions for stochastic evolution inclusions through a weak topology approach. Precisely, the study focuses on stochastic evolution inclusions characterized by multivalued…

Alternative iterative methods for a nonexpansive mapping in a Banach space are proposed and proved to be convergent to a common solution to a fixed point problem and a variational inequality. We give rates of asymptotic regularity for such…

Large time behavior of solutions to abstract differential equations is studied. The corresponding evolution problem is: $$\dot{u}=A(t)u+F(t,u)+b(t), \quad t\ge 0; \quad u(0)=u_0. \qquad (*)$$ Here $\dot{u}:=\frac {du}{dt}$, $u=u(t)\in H$,…

We study the semilinear Cauchy problem for complex-valued damped evolution equations \begin{align*} \partial_t^2u+(-\Delta)^{\sigma}u+(-\Delta)^{\delta}\partial_tu=u^p,\ \ u(0,x)=u_0(x),\ \partial_tu(0,x)=u_1(x), \end{align*} with…

We study the numerical approximation of stochastic evolution equations with a monotone drift driven by an infinite-dimensional Wiener process. To discretize the equation, we combine a drift-implicit two-step BDF method for the temporal…

We study the existence and uniqueness of Lp-bounded mild solutions for a class ofsemilinear stochastic evolutions equations driven by a real L\'evy processes withoutGaussian component not square integrable for instance the stable process…

In this paper, new implicit methods with reduced memory are developed for solving the time-dependent Boltzmann transport equation (BTE). One-group transport problems in 1D slab geometry are considered. The reduced-memory methods are…

In this paper, we prove the existence of a mild $L^p$-solution for the backward stochastic evolution inclusion (BSEI for short) of the form \begin{align*}%\label{BSDI3} \begin{cases} dY_t+AY_tdt\in G(t,Y_t,Z_t)dt+Z_tdW_t,\quad t\in [0,T]…

We consider the convergence behavior using the relaxed Peaceman-Rachford splitting method to solve the monotone inclusion problem $0 \in (A + B)(u)$, where $A, B: \Re^n \rightrightarrows \Re^n$ are maximal $\beta$-strongly monotone…

We prove that there is $x_{\phi}\in X$ for which (*)$\frac{d u(t)}{dt}= A u(t) + \phi (t) $, $u(0)=x$ has on $\r$ a mild solution $u\in C_{ub} (\r,X)$ (that is bounded and uniformly continuous) with $u(0)=x_{\phi}$, where $A$ is the…

It is well known that the non-autonomous scalar differential equation of evolution has a unique solution given by an elementary exponential function. In general there is no such analogous solution to the corresponding non-autonomous…

This paper is devoted to the study of periodic solutions for a semilinear Euler-Bernoulli beam equation with variable coefficients. Such mathematical model may be described the infinitesimal, free, undamped in-plane bending vibrations of a…

Given a linear closed but not necessarily densely defined operator $A$ on a Banach space $E$ with nonempty resolvent set and a multivalued map $F\colon I\times E\map E$ with weakly sequentially closed graph, we consider the…

We study the periodic solutions of the delay equation $\dot{x}(t)=f(x(t),x(t-1))$, where $f$ scalar is strictly monotone in the delayed component and has even-odd symmetry. We completely describe the global bifurcation structure of periodic…