Local uniqueness of m-bubbling sequences for the Gel'fand equation. Issue 6 (3rd June 2019)

• Record Type: Journal Article
• Authors: Bartolucci, Daniele; Jevnikar, Aleks; Lee, Youngae; Yang, Wen
• Is Part Of: Communications in partial differential equations. Volume 44:Issue 6(2019)
• Page Start: 447
• Page End: 466
• Publication Date: 2019-06-03
• Subjects: Blow up solutions -- Gel'fand equation -- local uniqueness; 35B32 -- 35J25 -- 35J61 -- 35J99. 82D15; Differential equations, Partial -- Periodicals; 515.353
• DOI: 10.1080/03605302.2019.1581801
• Languages: English
• ISSNs: 0360-5302

Abstract

Abstract: We consider the Gel'fand problem, { Δ w ε + ε 2 h e w ε = 0 in Ω, w ε = 0 on ∂ Ω, where h is a nonnegative function in Ω ⊂ R 2 . Under suitable assumptions on h and Ω, we prove the local uniqueness of m − bubbling solutions for any ε > 0 small enough.