The Dirichlet problem for supercritical biharmonic equations with power-type nonlinearity

被引：29
作者：
Ferrero, Alberto
Grunau, Hans-Christoph
机构：
[1] Otto Von Guericke Univ, Fak Math, D-39016 Magdeburg, Germany
[2] Univ Pisa, Dipartimento Matemat, I-56127 Pisa, Italy
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2007年 / 234卷 / 02期
关键词：
D O I：
10.1016/j.jde.2006.11.007
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
For a semilinear biharmonic Dirichlet problem in the ball with supercritical power-type nonlinearity, we study existence/nonexistence, regularity and stability of radial positive minimal solutions. Moreover, qualitative properties, and in particular the precise asymptotic behaviour near x = 0 for (possibly existing) singular radial solutions, are deduced. Dynamical systems arguments and a suitable Lyapunov (energy) function are employed. (c) 2006 Elsevier Inc. All rights reserved.
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页码：582 / 606
页数：25
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