The exact boundary behavior of solutions to singular nonlinear Lane–Emden–Fowler type boundary value problems. (February 2015)

• Record Type: Journal Article
• Authors: Zhang, Zhijun; Li, Bo; Li, Xiaohong
• Is Part Of: Nonlinear analysis. Volume 21(2015)
• Page Start: 34
• Page End: 52
• Publication Date: 2015-02
• Subjects: Semilinear elliptic equations -- A singular Dirichlet problem -- The positive solutions -- The boundary behavior; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2014.06.007
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper we analyze the exact boundary behavior of solutions to singular nonlinear Dirichlet problems − △ u = b ( x ) g ( u ) + λ a ( x ) f ( u ), u > 0, x ∈ Ω, u | ∂ Ω = 0, where Ω is a bounded domain with smooth boundary in R N, λ ≥ 0, g ∈ C 1 ( ( 0, ∞ ), ( 0, ∞ ) ), lim s → 0 + g ( s ) = ∞, b, a ∈ C loc α ( Ω ), are positive in Ω, may be vanishing or singular on the boundary, and f ∈ C ( [ 0, ∞ ), [ 0, ∞ ) ) . We reveal that the nonlinear term λ a ( x ) f ( u ) does not affect the first expansion of the classical solutions near the boundary to the problem for several kinds of functions a and b .