Gelfand type elliptic problems under Steklov boundary conditions

被引：12

作者：

Berchio, Elvise ^{[1
]}

Gazzola, Filippo ^{[1
]}

Pierotti, Dario ^{[1
]}

机构：

[1] Politecn Milan, Dipartimento Matemat, I-20133 Milan, Italy

来源：

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2010年 / 27卷 / 01期

关键词：

EXTREMAL SOLUTIONS; EQUATIONS; REGULARITY; GROWTH;

D O I：

10.1016/j.anihpc.2009.09.011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For a Gelfand type semilinear elliptic equation we extend some known results for the Dirichlet problem to the Steklov problem. This extension requires some new tools, such as non-optimal Hardy inequalities, and discovers some new phenomena, in particular a different behavior of the branch of solutions and three kinds of blow-up for large solutions in critical growth equations. We also show that small values of the boundary parameter play against strong growth of the nonlinear source. (C) 2009 Elsevier Masson SAS. All rights reserved.

引用

页码：315 / 335

页数：21

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