We investigate stable solutions of elliptic equations of the type where n≥ 2, s∈(0, 1), λ≥ 0
and f is any smooth positive superlinear function. The operator (− Δ) s stands for the …

Stable solutions are ubiquitous in differential equations. They represent meaningful
solutions from a physical point of view and appear in many applications, including …

We deal with symmetry properties for solutions of nonlocal equations of the type where
s∈(0, 1) and the operator (− Δ) s is the so-called fractional Laplacian. The study of this …

" Micro-and nanoelectromechanical systems (MEMS and NEMS), which combine electronics
with miniature-size mechanical devices, are essential components of modern technology. It …

" The book describes how functional inequalities are often manifestations of natural
mathematical structures and physical phenomena, and how a few general principles …

We study the extremal solution for the problem (-Δ)^ su= λ f (u)(-Δ) su= λ f (u) in Ω Ω, u ≡ 0
u≡ 0 in\mathbb R^ n ∖ Ω R n∖ Ω, where λ> 0 λ> 0 is a parameter and s ∈ (0, 1) s∈(0, 1) …

We consider the class of semistable solutions to semilinear equations− Δu= f (u) in a
bounded smooth domain Ω of\input amssym \BbbR^n (with Ω convex in some results). This …

Acta Mathematica 2020.224.2.1 Page 1 Acta Math., 224 (2020), 187–252 DOI: 10.4310/ACTA.2020.v224.n2.a1
c 2020 by Institut Mittag-Leffler. All rights reserved Stable solutions to semilinear elliptic …

We examine the elliptic system given by {equation}\label {system_abstract}-\Delta u= v^
p,\qquad-\Delta v= u^\theta,\qquad\{in}\IR^ N,{equation} for $1< p\le\theta $ and the fourth …

We consider the class of semi-stable positive solutions to semilinear equations− Δ u= f (u) in
a bounded domain Ω⊂ ℝ n of double revolution, that is, a domain invariant under rotations …