In this paper, we study the existence and concentration of positive solution for the following
class of fractional elliptic equation ϵ^ 2s (-Δ)^ s u+ V (z) u= f (u)\quad in\; R^ N, ϵ 2 s (-Δ) …

In this communication, three different forms of fractional nonlinear Schrödinger equations
have been constructed based on the notion of nonlocal generalized fractional momentum …

The general objective of the work is to study dynamics of dissipative solitons in the
framework of a one-dimensional complex Ginzburg-Landau equation (CGLE) of a fractional …

Abstract We introduce axisymmetric Airy-Gaussian vortex beams in a model of an optical
system based on the (2+ 1)-dimensional fractional Schrödinger equation (FSE) …

The aim of this book is to collect a set of results concerning nonlinear Schrödinger equations
in the whole space driven by fractional operators. The material presented here was mainly …

In this paper we consider the nonlinear fractional Schrödinger equations in presence of a
critical power nonlinearity and a subcritical term ε^ 2s (-Δ)^ s u+ V (x) u= f (u)+ u^ 2^* _s …

We consider the following class of fractional problems with unbalanced growth:{(− Δ) ps
u+(− Δ) qs u+ V (ε x)(| u| p− 2 u+| u| q− 2 u)= f (u) in RN, u∈ W s, p (RN)∩ W s, q (RN), u> 0 …

We consider here solutions of the nonlinear fractional Schr¨ odinger equation ε2s (−) su+ V
(x) u= up. We show that concentration points must be critical points for V. We also prove that …

Concentration phenomena for the nonlocal Schrödinger equation with Dirichlet datum Page 1
ANALYSIS & PDE msp Volume 8 No. 5 2015 JUAN DÁVILA, MANUEL DEL PINO, SERENA …

By using the penalization method and the Ljusternik–Schnirelmann theory, we investigate
the multiplicity of positive solutions of the following fractional Schrödinger equation ε^ 2s …