Large solutions of elliptic semilinear equations in the borderline case. An exhaustive and intrinsic point of view

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:431

Article

Alarcon, S.¹  Diaz, G.²  Rey, J. M.² 

[1] Univ Tecn Federico Santa Maria, Dept Matemat, Valparaiso, Chile

[2] Univ Complutense Madrid, Dept Matemat Aplicada, Inst Matemat Interdisciplinar, E-28040 Madrid, Spain

关键词: Large solutions;    Asymptotic behavior;    Boundary blow-up;   

DOI  :  10.1016/j.jmaa.2015.05.068

来源: Elsevier

【 摘 要 】

We revisit the problem Delta u = f (u) in Omega, u(x) -> infinity as x -> delta Omega, where Omega subset of R-N, N > 1, is a bounded smooth domain and f is an increasing and continuous function in R+ with f(0(+)) = 0 for which the Keller Osserman condition holds. We study uniqueness of solutions, extending known results about the boundary blow-up behavior of solutions. Furthermore, we obtain explicit representations for the second order terms in the explosive boundary expansion of solutions under intrinsic and direct assumptions. Our study is exhaustive including both ordinary and borderline cases providing new and sharp results. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free