Related papers: Concentration phenomena for the Schr\"odinger-Pois…

We consider the modification of a single particle Schr\"{o}dinger equation by the inclusion of an additional gravitational self-potential term which follows from the prescription that the' mass-density'that enters this term is given by $m…

In this paper we consider the fractional nonlinear Schr\"odinger equation $$\varepsilon^{2s}(-\Delta)^s v+ V(x) v= f(v), \quad x \in \mathbb{R}^N$$ where $s \in (0,1)$, $N \geq 2$, $V \in C(\mathbb{R}^N,\mathbb{R})$ is a positive potential…

We present two types of the hydrodynamic limit of the nonlinear Schr\"odinger-Chern-Simons (SCS) system. We consider two different scalings of the SCS system and show that each SCS system asymptotically converges towards the compressible…

It is shown that, for a large class of statistical mixtures, the Wigner-Poisson (or Hartree) system can be reduced to an effective Schroedinger-Poisson system, in which the Schroedinger equation contains a new nonlinearity. For the case of…

We study the existence of positive solutions for nonlocal systems in gradient form and set in the whole $\mathbb R^N$. A quasilinear fractional Schr\"odinger equation, where the leading operator is the $\frac Ns$-fractional Laplacian, is…

This paper studies the scattering matrix $\Sigma(E;\hbar)$ of the problem \[ -\hbar^2 \psi''(x) + V(x) \psi(x) = E\psi(x) \] for positive potentials $V\in C^\infty(\R)$ with inverse square behavior as $x\to\pm\infty$. It is shown that each…

We study the ergodic properties of Schr\"odinger operators on a compact connected Riemannian manifold $M$ without boundary in case that the underlying Hamiltonian system possesses certain symmetries. More precisely, let $M$ carry an…

We investigate the limiting behavior of solutions with infinitely many peaks to nonlinear Schr\"odinger equations [-epsilon^2 Delta u_epsilon + u_epsilon = u_epsilon^p, u_epsilon > 0 in R^n,] as epsilon -> 0, where p is Sobolev subcritical.…

In this work we analyze a class of nonlinear fractional elliptic systems involving Hardy--type potentials and coupled by critical Hardy-Sobolev--type nonlinearities in $\mathbb{R}^N$. Due to the lack of compactness at the critical exponent…

We analyze the Schr\"odinger operator in two-dimensions with an attractive potential given by a Bessel-Macdonald function. This operator is derived in the non-relativistic approximation of planar quantum electrodynamics (${\rm QED}_3$)…

The goal of this article is to obtain observability estimates for Schr{\"o}dinger equations in the plane R 2. More precisely, considering a 2$\pi$Z 2-periodic potential V $\in$ L $\infty$ (R 2), we prove that the evolution equation…

We consider a 3d cubic focusing nonlinear Schr\"odinger equation with a potential $$i\partial_t u+\Delta u-Vu+|u|^2u=0,$$ where $V$ is a real-valued short-range potential having a small negative part. We find criteria for global…

In this paper, we study the following nonlinear Schr\"{o}dinger system of Hamiltonian type \begin{equation*} \left\{\begin{array}{l} -\Delta u+V(x)u=\partial_v H(x,u,v)+\omega v, \ x \in \mathbb{R}^N, \\ -\Delta v+V(x)v=\partial_u…

In this paper, we are concerned with the following Schr\"{o}dinger-Poisson system with critical nonlinearity and critical nonlocal term due to the Hardy-Littlewood-Sobolev inequality \begin{equation}\begin{cases} -\Delta u+u+\lambda\phi…

We consider the following Schr\"odinger-Bopp-Podolsky system with critical and sublinear terms \begin{equation*} \begin{cases} - \Delta u+ u+Q(x)\phi u= \vert u\vert^4 u+ \lambda K(x)\vert u \vert^{p-1}u&\mbox{ in }\ \mathbb{R}^3 \smallskip…

In the present paper, we consider the Chern-Simons-Schr\"{o}dinger system \begin{equation} \left\{ \begin{aligned} &-\varepsilon^{2}\Delta u+V(x)u+(A_{0}+A_{1}^{2}+A_{2}^{2})u=|u|^{p-2}u,\,\,\,\,x\in \mathbb{R}^2,\\ &\partial_1 A_0 = A_2…

We prove the existence of solutions to the Schrodinger-Poisson system on a time interval independent of the Planck constant, when the doping profile does not necessarily decrease at infinity, in the presence of a subquadratic external…

In this article, we consider the infinite dimensional vector-valued resonant nonlinear Schr\"odinger system, which arises from the study of the asymptotic behavior of the defocusing nonlinear Schr\"{o}dinger equation on "wave guide"…

This paper is motivated by the study of a version of the so-called Schrodinger-Poisson-Slater problem: $$ - \Delta u + \omega u + \lambda (u^2 \star \frac{1}{|x|}) u=|u|^{p-2}u,$$ where $u \in H^1(\R^3)$. We are concerned mostly with $p \in…

We study the resonances of a two-by-two semiclassical system of one dimensional Schr\"odinger operators, near an energy where the two potentials intersect transversally, one of them being bonding, and the other one anti-bonding. Under an…