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We investigate the soliton dynamics for the fractional nonlinear Schrodinger 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.
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.
The semiclassical limit of a nonlinear focusing Schrodinger equation in presence of nonconstant electric and magnetic potentials V,A is studied by taking as initial datum the ground state solution of an associated autonomous elliptic equation. The co
This paper is devoted to prove the existence and nonexistence of positive solutions for a class of fractional Schrodinger equation in RN of the We apply a new methods to obtain the existence of positive solutions when f(u) is asymptotically linear with respect to u at infinity.
In this note, we give an alternative proof of the theorem on soliton selection for small energy solutions of nonlinear Schrodinger equations (NLS) which we studied in Anal. PDE 8 (2015), 1289-1349 and more recently in Annals of PDE (2021) 7:16. As
This article concerns the fractional elliptic equations begin{equation*}(-Delta)^{s}u+lambda V(x)u=f(u), quad uin H^{s}(mathbb{R}^N), end{equation*}where $(-Delta)^{s}$ ($sin (0,,,1)$) denotes the fractional Laplacian, $lambda >0$ is a parameter, $