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Research Article | Open Access

Entire positive k-convex solutions to k-Hessian type equations and systems

Shuangshuang Bai1, Xuemei Zhang1( ), Meiqiang Feng2
School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China
School of Applied Science, Beijing Information Science & Technology University, Beijing 100192, China
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Abstract

In this paper, we study the existence of entire positive solutions for the k-Hessian type equation

Sk(D2u+αI)=p(|x|)fk(u),x∈Rn

and system

{Sk(D2u+αI)=p(|x|)fk(v),x∈Rn,Sk(D2v+αI)=q(|x|)gk(u),x∈Rn,

where D2u is the Hessian of u and I denotes unit matrix. The arguments are based upon a new monotone iteration scheme.

Keywords

k-Hessian type equation and systementire positive k-convex solutionmonotone iterativeexistence

References

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Electronic Research Archive
Volume 30 Issue 2,
February 2022
Pages 481-491
DOI: 10.3934/era.2022025

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Cite this article:
Bai S, Zhang X, Feng M. Entire positive k-convex solutions to k-Hessian type equations and systems. Electronic Research Archive, 2022, 30(2): 481-491. https://doi.org/10.3934/era.2022025

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Received: 15 December 2021
Revised: 14 January 2022
Accepted: 21 January 2022
Published: 15 February 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)