Asymptotics for a high-energy solution of a supercritical problem. (February 2023)

• Record Type: Journal Article
• Authors: Colasuonno, Francesca; Noris, Benedetta
• Is Part Of: Nonlinear analysis. Volume 227(2023)
• Publication Date: 2023-02
• Subjects: 35J92 -- 35J20 -- 35B09 -- 35B45; Singular p-Laplacian equations -- Neumann boundary conditions -- Asymptotics of radial solutions; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2022.113166
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we deal with the equation − Δ p u + | u | p − 2 u = | u | q − 2 u for 1 < p < 2 and q > p, under Neumann boundary conditions in the unit ball of R N . We focus on the three positive, radial, and radially non-decreasing solutions, whose existence for q large is proved in Colasuonno et al. (2022). We detect the limit profile as q → ∞ of the higher energy solution and show that, unlike the minimal energy one, it converges to the constant 1. The proof requires several tools borrowed from the theory of minimization problems and accurate a priori estimates of the solutions, which are of independent interest.