Boundary behavior of large solutions to p-Laplacian elliptic equations. (February 2017)

• Record Type: Journal Article
• Authors: Zhang, Zhijun
• Is Part Of: Nonlinear analysis. Volume 33(2017)
• Page Start: 40
• Page End: 57
• Publication Date: 2017-02
• Subjects: p-Laplacian elliptic equations -- Large solutions -- Boundary behavior; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2016.05.008
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This paper is concerned with exact asymptotic behavior near the boundary of large solutions to quasilinear elliptic equations △ p u ( x ) = b ( x ) f ( u ( x ) ), x ∈ Ω, where Ω is a bounded smooth domain in R N, △ p u = div ( | ∇ u | p − 2 ∇ u ) with p > 1, and b ∈ C ( Ω ) is nonnegative in Ω, but may be vanishing or appropriately singular (including critical singular) on the boundary. We give one new condition near infinity on f which plays a crucial role in the boundary behavior of solutions.