34 research outputs found
Nonlinear fractional magnetic Schr\"odinger equation: existence and multiplicity
In this paper we focus our attention on the following nonlinear fractional
Schr\"odinger equation with magnetic field \begin{equation*}
\varepsilon^{2s}(-\Delta)_{A/\varepsilon}^{s}u+V(x)u=f(|u|^{2})u \quad \mbox{
in } \mathbb{R}^{N}, \end{equation*} where is a parameter,
, , is the fractional magnetic
Laplacian, and
are continuous potentials and
is a subcritical nonlinearity. By
applying variational methods and Ljusternick-Schnirelmann theory, we prove
existence and multiplicity of solutions for small.Comment: 23 page
Soliton dynamics for the Schrodinger-Newton system
We investigate the soliton dynamics for the Schrodinger-Newton system by
proving a suitable modulational stability estimates in the spirit of those
obtained by Weinstein for local equations.Comment: 10 page
Ground states for fractional magnetic operators
We study a class of minimization problems for a nonlocal operator involving
an external magnetic potential. The notions are physically justified and
consistent with the case of absence of magnetic fields. Existence of solutions
is obtained via concentration compactness.Comment: 22 pages, minor corrections and typos fixe
Quasilinear elliptic equations in \RN via variational methods and Orlicz-Sobolev embeddings
In this paper we prove the existence of a nontrivial non-negative radial
solution for a quasilinear elliptic problem. Our aim is to approach the problem
variationally by using the tools of critical points theory in an Orlicz-Sobolev
space. A multiplicity result is also given.Comment: 18 pages, 1 figur
On the logarithmic Schrodinger equation
In the framework of the nonsmooth critical point theory for lower
semi-continuous functionals, we propose a direct variational approach to
investigate the existence of infinitely many weak solutions for a class of
semi-linear elliptic equations with logarithmic nonlinearity arising in
physically relevant situations. Furthermore, we prove that there exists a
unique positive solution which is radially symmetric and nondegenerate.Comment: 10 page