Uniqueness of positive solutions of semilinear elliptic equations and related eigenvalue problems

被引：0
作者：
Pacella F. [1 ]
机构：
[1] Dipartimento di Matematica, Universitá di Roma La Sapienza, 00185 Roma
来源：
Milan Journal of Mathematics | 2005年 / 73卷 / 1期
关键词：
Asymptotic Behaviour; Eigenvalue Problem; Recent Result; Bounded Domain; Elliptic Equation;
D O I：
10.1007/s00032-005-0045-x
中图分类号：
学科分类号：
摘要：
In this paper we survey some recent results about the uniqueness of the solution of some semilinear elliptic Dirichlet problems in bounded domains. The presentation aims to emphasize the role of the geometrical properties of the second eigenfunction of the linearized problem in the study of the above question. This motivates the analysis of the asymptotic behaviour of these eigenfunctions and of the relative eigenvalues when the nonlinear term is a power with exponent close to the critical Sobolev exponent. © 2005 Birkhäuser Verlag, Basel/Switzerland.
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页码：221 / 236
页数：15
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