Existence of Positive Solutions for a Class of Almost Critical Problems on an Annulus

SIAM Journal on Mathematical Analysis 2026 Open access

Read full text
Authors: Gabriele Mancini, Giuseppe Mario Rago, Giusi Vaira
DOI: 10.1137/25m1834387
Cited by: 0
References: 36

Abstract

Abstract. In this paper we will consider multipeak positive solutions for a class of slightly subcritical or slightly supercritical elliptic problems on an annulus with Dirichlet boundary conditions. By using the explicit form of the Green function and of the Robin function on the annulus, we prove that the annulus becomes thinner and thinner as the number of bumps increases for the slightly subcritical case, while the hole of the annulus is very small for the slightly supercritical case.

Fields of Study & Subjects

Nonlinear Partial Differential Equations Nonlinear Differential Equations Analysis Advanced Mathematical Modeling in Engineering

Publication details

Journal / source
SIAM Journal on Mathematical Analysis
Volume
58
Issue
5
Pages
5100–5126
Publication date
16 September 2026
Language
EN