Ground States for the Fractional Schrödinger Equation

Radial Symmetry of Ground States for a Regional Fractional Nonlinear Schrödinger Equation

The aim of this paper is to study radial symmetry properties for ground state solutions of elliptic equations involving a regional fractional Laplacian, namely (−∆)ρ u+ u = f(u) in R, for α ∈ (0, 1). (1) In [9], the authors proved that problem (1) has a ground state solution. In this work we prove that the ground state level is achieved by a radially symmetry solution. The proof is carried out ...

The Nonlinear Schrödinger Equation Ground States on Product Spaces

Bound States of Two-dimensional Schrödinger-newton Equations

We prove an existence and uniqueness result for ground states and for purely angular excitations of two-dimensional Schrödinger-Newton equations. From the minimization problem for ground states we obtain a sharp version of a logarithmic Hardy-Littlewood-Sobolev type inequality.

Energy solutions and concentration problem of fractional Schrödinger equation

Soliton Dynamics for Fractional Schrödinger Equations

We investigate the soliton dynamics for the fractional nonlinear Schrödinger equation by a suitable modulational inequality. In the semiclassical limit, the solution concentrates along a trajectory determined by a Newtonian equation depending of the fractional diffusion parameter.