Boundary behavior of large solutions for semilinear elliptic equations with weights

Article type: Research Article

Authors: Zhang, Zhijun

Affiliations: School of Mathematics and Information Science, Yantai University, Yantai 264005, Shandong, P.R. China. E-mails: [email protected], [email protected]

Abstract: This paper is concerned with boundary blow-up elliptic problems △u=b(x)f(u), x∈Ω, u|∂Ω=+∞, where Ω is a bounded domain with smooth boundary in RN, and b∈Clocα(Ω) for some α∈(0,1) which is nonnegative nontrivial in Ω, but may be vanishing or appropriate singular (including critical singular) on ∂Ω. Under a new structure condition on f near infinity, we study the exact boundary behavior of such solutions.

Keywords: semilinear elliptic equations, boundary blow-up, the first expansions of solutions near the boundary

DOI: 10.3233/ASY-151345

Journal: Asymptotic Analysis, vol. 96, no. 3-4, pp. 309-329, 2016