The nonlinear Schroedinger equation: Solitons dynamics

In this paper we investigate the dynamics of solitons occurring in the nonlinear Schroedinger equation when a parameter h→0.We prove that under suitable assumptions, the soliton approximately follows the dynamics of a point particle, namely, the motion of its barycenterqh(t) satisfies the equation

     

Multifractal analysis of divergence points of deformed measure theoretical Birkhoff averages. II: Non-linearity, divergence points and Banach space valued spectra

During the past 10 years multifractal analysis has received an enormous interest. For a sequence n(φn) of functions φn:X→M on a metric space X, multifractal analysis refers to the study of the Hausdorff dimension of the level sets

     

Ornstein–Uhlenbeck operators with time periodic coefficients

We study the realization of the differential operator in the space of continuous time periodic functions, and in L ² with respect to its (unique) invariant measure. Here L(t) is an Ornstein-Uhlenbeck operator in , such that L(t + T) = L(t) for each .      

Existence of infinitely many large solutions for the nonlinear Schrödinger-Maxwell equations

In this paper, we study the nonlinear stationary Schrödinger-Maxwell equations

(∗)     

Stability of some waves in the dissipative Boussinesq system

In this paper we study analytically a class of waves in the variant of the classical dissipative Boussinesq system given by

     

The local variational principle of topological pressure for sub-additive potentials

Let (X,T) be a topological dynamical system and be a sub-additive potential on C(X,R). Let U be an open cover of X. Then for any T-invariant measure μ, let . The topological pressure for open covers U is defined for sub-additive potentials. Then we have a variational principle:

     

Attractors for nonautonomous 2D Navier-Stokes equations with less regular normal forces

First, the existence and structure of uniform attractors in H is proved for nonautonomous 2D Navier-Stokes equations on bounded domain with a new class of distribution forces, termed normal in (see Definition 3.1), which are translation bounded but not translation compact in . Then, the properties of the kernel section are investigated. Last, the fractal dimension is estimated for the kernel sections of the uniform attractors obtained.     

On random perturbation of some intersective sets

Given a subset S of Z and a sequence I = (I_n)_n=1^∞ of intervals of increasing length contained in Z, let

     

Uniqueness properties of solutions of Schrödinger equations

Under suitable assumptions on the potentials V and a, we prove that if u∈C([0,1],H¹) is a solution of the linear Schrödinger equation

     

On the support of solutions to the Ostrovsky equation with negative dispersion

In this article we prove that sufficiently smooth solutions of the Ostrovsky equation with negative dispersion:

     

On the support of solutions to the Ostrovsky equation with positive dispersion

In this paper we prove that sufficiently smooth solutions of the Ostrovsky equation with positive dispersion,

     

On the support of solutions to the Zakharov-Kuznetsov equation

In this article we prove that sufficiently smooth solutions of the Zakharov-Kuznetsov equation: