Orbital stability of standing wavesof Bose Einstein Condensates

We Proveexistence, symmetry and uniqueness of standing waves of a BCE with josephson junction. We also characterize the orbit of standing wavesComment: 1

On the necessity of the assumptions used to prove Hardy-Littlewood and Riesz Rearrangement Inequalities 1

We prove that supermodularity is a necessary condition for the generalized Hardy- Littlewood and Riesz rearrangement inequalities. We also show the necessity of the monotonicity of the kernels involved in the Riesz{type integral.Comment: 8 page

On the Nonlinear Schrodinger systems with local and nonlocal nolinearities Part1

We study well-posedness, local and global, existence of solutions for a general class of physically meaningful nonlinear Schr\"odinger systems with magnetic field involving local and nonlocal nonlinearities

Variational problems related to some fractional kinetic equations

We establish the existence and symmetry of all minimizers of a constrained variational problem involving the fractional gradient. This problem is closely connected to some fractional kinetic equations.Comment:

Generalized Polya-szego Inequality

In this paper we prove the Polya-Inequality for integrands depending on a function u and its gradient. We also establish cases of equality in this symmetrization inequality.Comment: 10

On Schr\"odinger Systems with Local and Nonlocal Nonlinearities - Part II

In this second part, we establish the existence of special solutions of the nonlinear Schr\"odinger system studied in the first part when the diamagnetic field is nul. We also prove some symmetry properties of these ground states solutions.Comment: 16 page

Orbital stability of standing waves of some m-coupled nonlinear Schrodinger equations

We extend the notion of orbital stability to systems of nonlinear Schrodinger equations, then we prove this property under suitable assumptions of the local nonlinearity involved.Comment: 1

Symmetric Ground States Solutions of M-Coupled Nonlinear Schrodinger Equations

We prove the existence of radial and radially decreasing ground states of an m-coupled nonlinear Schrodinger equation with a general nonlinearity

Complementary study of the standing wave solutions of the Gross-Pitaevskii equation in dipolar quantum gases

We study the stability of the standing wave solutions of a Gross-Pitaevskii equation describing Bose-Einstein condensation of dipolar quantum gases and characterize their orbit. As an intermediate step, we consider the corresponding constrained minimization problem and establish existence, symmetry and uniqueness of the ground state solutions.Comment: 10 page

A weak-strong convergence property and symmetry of minimizers of constrained variational problems in RN\mathbb{R}^N

We prove a weak-strong convergence result for functionals of the form $\int_{\mathbb{R}^N} j(x, u, Du)\,dx$ on $W^{1,p}$, along equiintegrable sequences. We will then use it to study cases of equality in the extended Polya-Szeg\"o inequality and discuss applications of such a result to prove the symmetry of minimizers of a class of variational problems including nonlocal terms under multiple constraints.Comment: 25 page