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Advanced Nonlinear Studies

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Two Classes of Nonlinear Singular Dirichlet Problems with Natural Growth: Existence and Asymptotic Behavior

Zhijun Zhang
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  • School of Mathematics and Information Science, Yantai University, Yantai 264005, Shandong, P. R. China
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Published Online: 2019-08-27 | DOI: https://doi.org/10.1515/ans-2019-2054


This paper is concerned with the existence, uniqueness and asymptotic behavior of classical solutions to two classes of models -u±λ|u|2uβ=b(x)u-α, u>0, xΩ, u|Ω=0, where Ω is a bounded domain with smooth boundary in N, λ>0, β>0, α>-1, and bClocν(Ω) for some ν(0,1), and b is positive in Ω but may be vanishing or singular on Ω. Our approach is largely based on nonlinear transformations and the construction of suitable sub- and super-solutions.

Keywords: Semilinear Elliptic Equations; Singular Dirichlet Problems; Classical Solutions; Existence; Uniqueness; Asymptotic Behavior

MSC 2010: 35J25; 35J65; 35J67


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About the article

Received: 2019-04-29

Revised: 2019-06-24

Accepted: 2019-06-26

Published Online: 2019-08-27

Funding Source: National Natural Science Foundation of China

Award identifier / Grant number: 11571295

This work is supported in part by NSF of P. R. China under grant 11571295.

Citation Information: Advanced Nonlinear Studies, ISSN (Online) 2169-0375, ISSN (Print) 1536-1365, DOI: https://doi.org/10.1515/ans-2019-2054.

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