Related papers: Existence results for a non-relativistic Chern-Sim…
Using direct methods of the calculus of variations we establish the existence of an infinite class of spherically-symmetric solutions to the multi-field Schr\"odinger-Poisson system. This is achieved by proving that the energy functional…
The Chern-Simons theories on a noncommutative plane, which is shown to be describing the quantum Hall liquid, is considered. We introduce matter fields fundamentally coupled to the noncommutative Chern-Simons field. Exploiting BPS equations…
We investigate the existence of non-topological solutions $(u_1,u_2)$ satisfying $$u_{i}(x)=-2\beta_i\ln|x|+O(1),\quad\text{as }|x|\rightarrow +\infty,$$ such that $\beta_i>1$ and $$(\beta_1-1)(\beta_2-1)>(N_1+1)(N_2+1),$$ for a…
We are concerned with super-Liouville equations on the two sphere, which have variational structure with a strongly-indefinite functional. We prove the existence of non-trivial solutions by combining the use of Nehari manifolds, balancing…
We propose a new nonrelativistic Chern-Simons theory based on a simple modification of the standard Lagrangian. This admits asymptotically nonvanishing field configurations and is applicable to the description of systems of repulsive…
In this paper we prove a Liouville theorem for the Chern--Simons--Schr{\"o}dinger equation. This result is consistent with the soliton resolution conjecture for initial data that does not lie in a weighted space. See [KKO22] for the soliton…
It is shown that the non-relativistic `Dirac' equation of L\'evy-Leblond, we used recently to describe a spin $1/2$ field interacting non-relativistically with a Chern-Simons gauge field, can be obtained by lightlike reduction from $3+1$…
The non-relativistic Maxwell-Chern-Simons model recently introduced by Manton is shown to admit self-dual vortex solutions with non-zero electric field. The interrelated ``geometric'' and ``hidden'' symmetries are explained. The theory is…
We consider a singular Liouville equation on a compact surface, arising from the study of Chern-Simons vortices in a self dual regime. Using new improved versions of the Moser-Trudinger inequalities (whose main feature is to be scaling…
The interaction of a spin 1/2 particle (described by the non-relativistic "Dirac" equation of L\'evy-Leblond) with Chern-Simons gauge fields is studied. It is shown, that similarly to the four dimensional spinor models, there is a…
We use localization techniques to compute the expectation values of supersymmetric Wilson loops in Chern-Simons theories with matter. We find the path-integral reduces to a non-Gaussian matrix model. The Wilson loops we consider preserve a…
We consider a class of singular Liouville equations on compact surfaces motivated by the study of Electroweak and Self-Dual Chern-Simons theories, the Gaussian curvature prescription with conical singularities and Onsager's description of…
We consider here the simplified Ericksen-Leslie system on the whole three-dimensional space. This system deals with the incompressible Navier-Stokes equations strongly coupled with a harmonic map flow which models the dynamical behavior for…
We prove symmetry and uniqueness results for three classes of Liouville-type problems arising in geometry and mathematical physics: asymmetric Sinh-Gordon equation, cosmic string equation and Toda system, under certain assumptions on the…
The density-matrix and Heisenberg formulations of quantum mechanics follow--for unitary evolution--directy from the Schr"odinger equation. Nevertheless, the symmetries of the corresponding evolution operator, the Liouvillian L=i[.,H], need…
We study a system of equations arising in the Chern-Simons model on finite graphs. Using the iteration scheme and the upper and lower solutions method, we get existence of solutions in the non-critical case. The critical case is dealt with…
We have studied the noncommutative extension of the relativistic Chern-Simons-Higgs model, in the first non-trivial order in $\theta$, with only spatial noncommutativity. Both Lagrangian and Hamiltonian formulations of the problem have been…
We study the resonant prescribed T-curvature problem on a compact 4-dimensional Riemannian manifold with boundary. We derive sharp energy and gradient estimates of the associated Euler-Lagrange functional to characterize the critical points…
We investigate a class of quasi-linear nonlocal problems, including as a particular case semi-linear problems involving the fractional Laplacian and arising in the framework of continuum mechanics, phase transition phenomena, population…
We consider the Toda system on a compact surface. We give existence and multiplicity results, using variational and Morse-theoretical methods. It is the first existence result when some of the coefficients of the singularities are allowed…