We prove the uniqueness and nondegeneracy of least energy solutions of a fractional
Dirichlet semilinear problem in any ball and in more general sufficiently large symmetric …

We prove uniqueness of least-energy solutions for a class of semilinear equations driven by
the fractional laplacian, under homogeneous Dirichlet exterior conditions, when the …

We study the asymptotic behavior of solutions to various Dirichlet sublinear-type problems
involving the fractional Laplacian when the fractional parameter s tends to zero. Depending …

In this paper we study convexity properties for quasilinear Lane-Emden-Fowler equations of
the type $$\begin {cases}-\Delta_p u= a (x) u^ q &\quad\hbox {in $\Omega $},\\u> 0 …

Let $ u $ be either a second eigenfunction of the fractional $ p $-Laplacian or a least energy
nodal solution of the equation $(-\Delta)^ s_p\, u= f (u) $ with superhomogeneous and …

The main purpose of this work is to study a non-local scalar field equation in bounded
domains. More precisely we consider the semi-linear fractional elliptic problem:(− Δ) su= λ …

We analyze the shape of radial second Dirichlet eigenfunctions of fractional Schr\" odinger
type operators of the form $(-\Delta)^ s+ V $ in the unit ball $ B $ in $\mathbb {R}^ N $ with a …

We study the optimal boundary regularity of solutions to Dirichlet problems involving the
logarithmic Laplacian. Our proofs are based on the construction of suitable barriers via the …

We prove that positive solutions u∈ Hs (RN) to the equation (−∆) su+ u= up in RN are
nonradially nondegenerate, for all s∈(0, 1), N≥ 1 and p> 1 strictly smaller than the critical …

We consider the uniqueness of the following positive solutions of $ m $-Laplacian
equation:\begin {equation}\left\{\begin {aligned}-\Delta _m u&=\lambda u^{m-1}+ u^{p …