Boundary blow-up in nonlinear elliptic equations of Bieberbach-Rademacher type期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Boundary blow-up in nonlinear elliptic equations of Bieberbach-Rademacher type

Authors:	Florica-Corina Cî rstea Vicentiu Radulescu

Institution:	Department of Mathematics, The Australian National University, Canberra, ACT 0200, Australia ; Department of Mathematics, University of Craiova, 200585 Craiova, Romania

Abstract:	We establish the uniqueness of the positive solution for equations of the form $-\Delta u=au-b(x)f(u)$ in $\Omega$ , $u\vert _{\partial\Omega}=\infty$ . The special feature is to consider nonlinearities whose variation at infinity is not regular (e.g., $\exp(u)-1$ , $\sinh(u)$ , $\cosh(u)-1$ , $\exp(u)\log(u+1)$ , $u^\beta \exp(u^\gamma)$ , $\beta\in {\mathbb{R}}$ , $\gamma>0$ or $\exp(\exp(u))-e$ ) and functions $b\geq 0$ in $\Omega$ vanishing on $\partial\Omega$ . The main innovation consists of using Karamata's theory not only in the statement/proof of the main result but also to link the nonregular variation of at infinity with the blow-up rate of the solution near $\partial\Omega$ .

Keywords:	Large solutions boundary blow-up regular variation theory

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