We consider positive solutions of a fractional Lane–Emden-type problem in a bounded
domain with Dirichlet conditions. We show that uniqueness and nondegeneracy hold for the …

In this paper we prove Bourgain-Brezis-Mironescu's type results (cf.[4])(BBM for short) for an
energy functional which is strongly related to the pseudo anisotropic p-Laplacian. We also …

We study the limiting behavior of solutions to boundary value nonlinear problems involving
the fractional Laplacian of order 2 s when the parameter s tends to zero. In particular, we …

In this paper we deal with the stability of solutions to fractional p-Laplace problems with
nonlinear sources when the fractional parameter s goes to 1. We prove a general …

We study existence and convergence properties of least-energy symmetric solutions (less)
to the pure critical exponent problem (-Δ) s⁢ us=| us| 2 s⋆-2⁢ us, us∈ D 0 s⁢(Ω), 2 s⋆:= 2⁢ …

Let us denote a solution of the fractional Poisson problem (-Δ) sus= f in Ω, us= 0 on RN\Ω,
where N≥ 2 and Ω⊂ RN is a bounded domain of class C 2. We show that the solution …

This paper is devoted to the existence, nonexistence and multiplicity of solutions for a
fractional p-Kirchhoff equation with the critical Sobolev exponent involving competitive …

We consider the nonlinear fractional problem (-Δ)^ s u+ V (x) u= f (x, u) &\quad in R^ N (-Δ)
su+ V (x) u= f (x, u) in RN We show that ground state solutions converge (along a …

Inspired by some experimental (numerical) works on fractional diffusion PDEs, we develop a
rigorous framework to prove that solutions to the fractional Navier–Stokes equations, which …

We introduce a general coupled system of parabolic equations with quadratic nonlinear
terms and diffusion terms defined by fractional powers of the Laplacian operator. We …