Asymptotic behavior of least energy solutions for a critical elliptic system
Journal
International Mathematics Research Notices
Journal Volume
2015
Journal Issue
21
Pages
11045-11082
Date Issued
2015
Author(s)
Chen, Z.
Abstract
We study the asymptotic behavior of positive least energy solutions to a two coupled elliptic system with Sobolev critical exponents. This system is related to coupled nonlinear Schrödinger equations with critical exponents for Bose–Einstein condensates, and can be also seen as a counterpart of the classical Brézis–Nirenberg problem. There are three kinds of asymptotic behaviors for positive solutions of two coupled systems: (i) both two components converge; (ii) one component converges while the other one blows up; (iii) both two components blow up at some points and can be controlled by global bubbling solutions. In this paper, we prove that any of these three types happens under different circumstances for least energy solutions.
SDGs
Type
journal article