Boundary concentrating solutions for a Hénon-like equation. Issue 1 (30th January 2015)

• Record Type: Journal Article
• Authors: Peng, Shuangjie; Pi, Huirong
• Is Part Of: Proceedings. Volume 145:Issue 1(2015)
• Page Start: 175
• Page End: 201
• Publication Date: 2015-01-30
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1017/S0308210513000553
• Languages: English
• ISSNs: 0308-2105

Abstract

Abstract : This paper is concerned with the existence and qualitative property of solutions for a Hénon-like equation where Ω = { x ∈ ℝ N : 1 < | x | < 3} with N ≥ 4, 2* = 2 N /( N − 2), τ > 0 and ε > 0 is a small parameter. For any given k ∈ ℤ +, we construct positive solutions concentrating simultaneously at 2 k different points for ε sufficiently small, among which k points are near the interior boundary { x ∈ ℝ N : | x | = 1} and the other k points are near the outward boundary { x ∈ ℝ N : | x | = 3}. Moreover, the 2 k points tend to the boundary of Ω as ε goes to 0.