A global compactness result for a mixed boundary value problem in half cylinder. (April 2016)

• Record Type: Journal Article
• Authors: Fang, Fei; Xu, Jiankai
• Is Part Of: Nonlinear analysis. Volume 28(2016)
• Page Start: 184
• Page End: 191
• Publication Date: 2016-04
• Subjects: Critical growth -- Compactness -- P.S. sequence; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2015.07.020
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: Let Ω be a bounded smooth domain in R N with N ≥ 2, C = Ω × ( 0, ∞ ) and { u n } ⊂ H 0, L 1 ( C ) be a (P.S.) sequence of the functional I λ ( u ) = 1 2 ∫ C ∣ ∇ u ∣ 2 d x d y − λ 2 ∫ Ω × { 0 } ∣ u ∣ 2 d x − N − 1 2 N ∫ Ω × { 0 } ∣ u ∣ 2 N N − 1 d x, λ ∈ R . We study the limit behaviour of u n and obtain a global compactness result.