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The fractional discrete nonlinear Schrodinger equation
(Elsevier, 2020)
We examine a fractional version of the discrete nonlinear Schrodinger (dnls) equation, where the usual discrete laplacian is replaced by a fractional discrete laplacian. This leads to the replacement of the usual ...
Bubbling solutions for nonlocal elliptic problems
(European Mathematical Society Publishing House, 2017)
We investigate bubbling solutions for the nonlocal equation Aω s u = up, u > 0 in ω, under homogeneous Dirichlet conditions, where ω is a bounded and smooth domain. The operator As ω stands for two types of nonlocal ...
The two-dimensional fractional discrete nonlinear Schrödinger equation
(Elsevier, 2020)
We study a fractional version of the two-dimensional discrete nonlinear Schrodinger (DNLS) equation, where the usual discrete Laplacian is replaced by its fractional form that depends on a fractional exponent s that ...
Ground states and concentration phenomena for the fractional Schrodinger equation
(IOP Publishing, 2015)
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 if the potential V is coercive ...
Non-linear Schrodinger equation with non-local regional diffusion
(Springer, 2015)
In this article we are interested in the nonlinear Schrodinger equation with non-local regional difussion
epsilon(2 alpha)(-Delta)(rho)(alpha)u + u = f (u) in R-n,
u epsilon H-alpha(R-n),
where f is a super-linear ...
Scalar field equation with non-local diffusion
(Springer, 2015)
In this paper we are interested on the existence of ground state solutions for fractional field equations of the form
integral (I - Delta)(alpha) u = f(x, u) in IRN, u > 0 in IRN, lim(vertical bar x vertical bar ...
Interior regularity results for zeroth order operators approaching the fractional Laplacian
(Springer New York LLC, 2018)
In this article we are interested in interior regularity results for the solution μ∈∈ C(Ω¯) of the Dirichlet problem {μ=0inΩc,I∈(μ)=f∈inΩ where Ω is a bounded, open set and f∈∈ C(Ω¯) for all є ∈ (0, 1). For some σ ∈ (0, ...
Uniform Equicontinuity for a Family of Zero Order Operators Approaching the Fractional Laplacian
(Taylor & Francis, 2015)
In this paper we consider a smooth bounded domain < subset of>(N) and a parametric family of radially symmetric kernels K-epsilon: (N)(+) such that, for each epsilon (0, 1), its L-1-norm is finite but it blows up as epsilon ...
Symmetry results for positive solutions of mixed integro-differential equations
(Academic Press-Elsevier, 2016)
In this paper, we study symmetry property for positive solutions of mixed integro-differential equations
[GRAPHICS]
where N, M >= 1, x is an element of B-1(N)(0) = {x is an element of R-N : vertical bar x vertical ...
Delaunay-type singular solutions for the fractional Yamabe problem
(Springer, 2017)
We construct Delaunay-type solutions for the fractional Yamabe problem with an isolated singularity(Formula Presented.)We follow a variational approach, in which the key is the computation of the fractional Laplacian in ...