Asymptotic behavior of least energy solutions to the Lane-Emden system near the critical hyperbola

Abstract

We consider the Lane-Emden system

{-Delta u = v(p) in Omega, -Delta v = u(q) in Omega, u, v > 0 in Omega, u = v = 0 on partial derivative Omega

where 12 is a smooth bounded domain in R-n for n >= 3 and 0 < p < q < infinity. The asymptotic behavior of least energy solutions near the critical hyperbola was studied by Guerra [17] when p >= 1 and the domain is convex. In this paper, we cover all the remaining cases p < 1 and extend the results to arbitrary smooth bounded domains. (C) 2019 Elsevier Masson SAS. All rights reserved.