Proceedings of the American Mathematical Society

Author(s): Xiaohu Ji; Jiguang Bao
Journal: Proc. Amer. Math. Soc. 138 (2010), 175-188.
MSC (2000): Primary 35J60, 35J85
Posted: September 3, 2009
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Abstract: In this paper, we discuss the solvability of the Hessian inequality $\sigma^{\frac{1}{k}}_{k}(\lambda (D^{2}u)) \ge f(u)$ on the entire space $\mathbb{R}^{n}$ and provide a necessary and sufficient condition, which can be regarded as a generalized Keller-Osserman condition.

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 35J60, 35J85

Xiaohu Ji
Affiliation: School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, People's Republic of China
Email: Ji.Xiaohu@hotmail.com

Jiguang Bao
Affiliation: School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, People's Republic of China
Email: jgbao@bnu.edu.cn

DOI: 10.1090/S0002-9939-09-10032-1
PII: S 0002-9939(09)10032-1
Keywords: Hessian equation, subsolution, existence, nonexistence, Keller-Osserman condition
Received by editor(s): February 20, 2009
Posted: September 3, 2009
Additional Notes: This work was supported by the National Natural Science Foundation of China (10671022) and the Doctoral Programme Foundation of the Institute of Higher Education of China (20060027023).
Communicated by: Matthew J. Gursky
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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