Global bifurcation and convex solutions for the Monge-Ampère equation

We study the following Monge-Ampère equation{(det⁡(D2u))1N=λf(−u)inΩ,u=0on∂Ω by bifurcation technique. We establish some results about the existence, nonexistence, uniqueness and multiplicity of convex solutions for this problem. Our results generalize and improve many important known results from p...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 491; no. 2; p. 124389
Main Authors Luo, Hua, Cao, Xiaofei, Dai, Guowei
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.11.2020
Subjects
Bifurcation
Convex solution
Monge-Ampère equation
Bifurcation
Monge-Ampère equation
Convex solution
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Summary:We study the following Monge-Ampère equation{(det⁡(D2u))1N=λf(−u)inΩ,u=0on∂Ω by bifurcation technique. We establish some results about the existence, nonexistence, uniqueness and multiplicity of convex solutions for this problem. Our results generalize and improve many important known results from previous literature.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2020.124389