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- W2885452766 abstract "We consider the following singular semilinear problem begin{document}$left{ begin{array}{l} - Delta u(x) = a(x){u^sigma }(x),{rm{ }}x in Omega backslash { 0} ({rm{in;the;distributional;sense}}),;u > 0,{rm{ on}};Omega backslash { 0} ,mathop {lim }limits_{left| x right| to 0} frac{{u(x)}}{{ln left| x right|}} = 0,u(x) = 0,;x in partial Omega ,end{array} right.$ end{document} where $σ <1,$ $Ω $ is a bounded regular domain in $mathbb{R}^{2}$ with $0∈ Ω .$ The weight function $a(x)$ is requiredto be positive and continuous in $Ω backslash {0}$ with thepossibility to be singular at $x = 0$ and/or at the boundary $partial Ω. $ When the function $a$ satisfies sharp estimates related to Karamataclass, we prove the existence and global asymptotic behavior of a positivecontinuous solution on $overline{Ω }backslash {0}$ which couldblow-up at $0$." @default.
- W2885452766 created "2018-08-22" @default.
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- W2885452766 date "2019-01-01" @default.
- W2885452766 modified "2023-10-16" @default.
- W2885452766 title "Singular solutions of a nonlinear equation in a punctured domain of <inline-formula><tex-math id=M1>begin{document}$mathbb{R}^{2}$end{document}</tex-math></inline-formula>" @default.
- W2885452766 doi "https://doi.org/10.3934/dcdss.2019012" @default.
- W2885452766 hasPublicationYear "2019" @default.
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