Boundary blow-up solutions to the k-Hessian equation with a weakly superlinear nonlinearity

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:464

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;    Singular weight function;   

DOI  :  10.1016/j.jmaa.2018.04.014

来源: Elsevier

【 摘 要 】

By constructing new sub- and super-solutions, we are concerned with determining values of beta, for which there exist k-convex solutions to the boundary blow-up k-Hessian problem S-k(D(2)u(x)) = H(x)[u(x)](k)[ln u(x)](beta) > 0 for x is an element of Omega SZ, u(x) -> +infinity as dist(x,partial derivative Omega) -> 0. Here k is an element of {1, 2, ..., N}, S-k (D-u(2)) is the k-Hessian operator, beta > 0 and Omega is a smooth, bounded, strictly convex domain in R-N (N >= 2). We suppose that the nonlinearity behaves like u(k) ln(beta) as u -> infinity, which is more complex and difficult to deal with than the nonlinearity grows like u(p) with p > k or faster at infinity. Further, several new results of nonexistence, global estimates and estimates near the boundary for the solutions are also given. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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