相关论文: Ground states for fractional magnetic operators

We investigate the existence, multiplicity and concentration of nontrivial solutions for the following fractional magnetic Kirchhoff equation with critical growth: \begin{equation*} \left(a\varepsilon^{2s}+b\varepsilon^{4s-3}…

This doctoral thesis is devoted to the analysis of some minimization problems that involve nonlocal functionals. We are mainly concerned with the $s$-fractional perimeter and its minimizers, the $s$-minimal sets. We investigate the behavior…

We construct solutions to a class of Schr\"{o}dinger equations involving the fractional laplacian. Our approach is variational in nature, and based on minimization on the Nehari manifold.

In this paper, we study the existence of minimizers of the Sobolev quotient for a class of nonlocal operators with an orthotropic structure having different exponents of integrability and different orders of differentiability. Our method is…

In this paper we study the existence of minimizers for interaction energies with the presence of external potentials. We consider a class of subharmonic interaction potentials, which include the Riesz potentials $|{\bf…

In this paper, we investigate the existence of weak solution for a fractional type problems driven by a nonlocal operator of elliptic type in a fractional Orlicz-Sobolev space, with homogeneous Dirichlet boundary conditions. We first extend…

We revisit the basic variational formulation of the minimization problem associated with the micromagnetic energy, with an emphasis on the treatment of the stray field contribution to the energy, which is intrinsically non-local. Under…

Recently, great attention has been focused on the study of fractional and non-local operators of elliptic type, both for pure mathematical research and in view of concrete real-world applications. Our problem is related to the fractional…

In this article, we establish some conditions for the boundedness of fractional integral operators on the vanishing generalized weighted Morrey spaces. We also investigate corresponding commutators generated by BMO functions.

A case of non-minimal couplings between gravity and electromagnetic fields is presented. The field equations are worked out in the language of exterior differential forms. An exact charge screening class of solutions is given with a…

We consider systems of weakly coupled Schr\"odinger equations with nonconstant potentials and we investigate the existence of nontrivial nonnegative solutions which concentrate around local minima of the potentials. We obtain sufficient and…

In this paper, we study the existence of positive non-decreasing radial solutions of a nonlocal non-standard growth problem ruled by the fractional $g$-Laplace operator with exterior Neumann condition. Our argument exploits some properties…

It has recently been proven that certain effective wavefunctions in fractional quantum mechanics and condensed matter do not have a locally conserved current; as a consequence, their coupling to the electromagnetic field leads to extended…

We construct solutions to the nonlinear magnetic Schr\"odinger equation $$ \left\{ \begin{aligned} - \varepsilon^2 \Delta_{A/\varepsilon^2} u + V u &= \lvert u\rvert^{p-2} u & &\text{in}\ \Omega,\\ u &= 0 & &\text{on}\ \partial\Omega,…

Delocalization problem for a two-dimensional non-interacting electron system is studied under a random magnetic field. With the presence of a random magnetic field, the Hall conductance carried by each eigenstate can become nonzero and…

In this paper, we study the following nonlocal problem in fractional Orlicz Sobolev spaces \begin{eqnarray*} (-\Delta_{\Phi})^{s}u+V(x)a(|u|)u=f(x,u),\quad x\in\mathbb{R}^N, \end{eqnarray*} where $(-\Delta_{\Phi})^{s}(s\in(0, 1))$ denotes…

We consider the problem of existence of constrained minimizers for the focusing mass-subcritical Half-Wave equation with a defocusing mass-subcritical perturbation. We show the existence of a critical mass such that minimizers do exist for…

We study the problem of a charged particle in the presence of a uniform magnetic field plus a vortex in noncommutative planar space considering the two possible non-commutative extensions of the corresponding Hamiltonian, namely the…

Microcausality -- the vanishing of commutators outside the lightcone -- is a fundamental property of relativistic quantum field theories. We derive its implications for two-point functions of scalar operators on {\it Lorentz-breaking}…

An energy functional for orbital based $O(N)$ calculations is proposed, which depends on a number of non orthogonal, localized orbitals larger than the number of occupied states in the system, and on a parameter, the electronic chemical…