A sufficient and necessary condition of existence of blow-up radial solutions for a k-Hessian equation with a nonlinear operator

Xinguang Zhang; Lishan Liu; Yonghong Wu; Yujun Cui

doi:10.15388/namc.2020.25.15736

Articles

Xinguang Zhang

Yantai University

https://orcid.org/0000-0001-9250-6823

Lishan Liu

Qufu Normal University

https://orcid.org/0000-0001-8541-1017

Yonghong Wu

Curtin University of Technology

Yujun Cui

Shandong University of Science and Technology

https://orcid.org/0000-0002-6688-4748

Published 2020-01-10

https://doi.org/10.15388/namc.2020.25.15736

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Keywords

k-Hessian equation
existence and nonexistence
sufficient and necessary condition
blow-up solutions

How to Cite

Zhang X., Liu L., Wu Y. and Cui Y. (2020) “A sufficient and necessary condition of existence of blow-up radial solutions for a k-Hessian equation with a nonlinear operator”, Nonlinear Analysis: Modelling and Control, 25(1), pp. 126–143. doi: 10.15388/namc.2020.25.15736.

Abstract

In this paper, we establish the results of nonexistence and existence of blow-up radial solutions for a k-Hessian equation with a nonlinear operator. Under some suitable growth conditions for nonlinearity, the result of nonexistence of blow-up solutions is established, a sufficient and necessary condition on existence of blow-up solutions is given, and some further results are obtained.

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