Entire subsolutions of a kind of k-Hessian type equations with gradient terms

2022/08/23 by Jingwen Ji, Feida Jiang, Ji, Jingwen +3
Mathematics · #35J60 #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2208.11103

openalex publication_date 2022/08/23 · openalex created_date 2022/08/25 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider a kind of k-Hessian type equations S_k^(1)/(k)(D²u+μ|D u|I)= f(u) in ℝⁿ, and provide a necessary and sufficient condition of f on the existence and nonexistence of entire admissible subsolutions, which can be regarded as a generalized Keller-Osserman condition. The existence and nonexistence results are proved in different ranges of the parameter μ respectively, which embrace the standard Hessian equation case (μ=0) by Ji and Bao (Proc Amer Math Soc 138: 175--188, 2010) as a typical example. The difference between the semilinear case (k=1) and the fully nonlinear case (k≥ 2) is also concerned.

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