Asymptotic behavior up to the second order term of solutions to quasilinear elliptic singular problems. (November 2016)

• Record Type: Journal Article
• Authors: Giarrusso, Ester; Porru, Giovanni
• Is Part Of: Nonlinear analysis. Volume 145(2016)
• Page Start: 49
• Page End: 67
• Publication Date: 2016-11
• Subjects: 35J25 -- 35J61 -- 35B40; Singular elliptic equations -- Second order boundary approximation; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2016.07.005
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: Let Ω ⊂ R N be a bounded smooth domain. We prove the existence of a positive solution to the problem Δ u = − u − γ | ∇ u | q in Ω, u = 0 on ∂ Ω, with γ > 1 and 0 < q < 1 . Furthermore, for γ > 3 and 0 < q ≤ ( γ − 3 ) / ( γ − 2 ) we find asymptotic expansions up to the second order of a solution u in terms of the distance from x to the boundary ∂ Ω .