The existence and asymptotic behavior of boundary blow-up solutions to the k-Hessian equation

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:267

Article

Zhang, Xuemei¹  Feng, Meiqiang² 

[1] North China Elect Power Univ, Dept Math & Phys, Beijing 102206, Peoples R China

[2] Beijing Informat Sci & Technol Univ, Sch Appl Sci, Beijing 100192, Peoples R China

关键词: k-Hessian equation;    Boundary blow up;    Sub-supersolution method;    k-convex solution;    Existence and asymptotic behavior;   

DOI  :  10.1016/j.jde.2019.05.004

来源: Elsevier

【 摘 要 】

In this paper we consider the existence and asymptotic behavior of k-convex solution to the boundary blow-up k-Hessian problem S-k(D(2)u) = H(x) f(u) for x epsilon Omega, u(x) -> +infinity as dist(x, partial derivative Omega) -> 0, where k epsilon {1, 2, . . . , N}, S-k(D(2)u) is the k-Hessian operator, Omega is a smooth, bounded, strictly convex domain in R-N(N >= 2), H epsilon C-infinity (Omega) is positive in Omega, but is not necessarily bounded on partial derivative Omega, and fis a smooth positive function that satisfies the so-called Keller-Osserman condition. Further results are obtained for the special case that Omega is a ball. Our approach to show the existence and asymptotic behavior, exploits the method of sub-and super-solutions and Karamata regular variation theory. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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