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.
Uniqueness of positive solutions of semilinear elliptic equations and related eigenvalue problems / Pacella, Filomena. - In: MILAN JOURNAL OF MATHEMATICS. - ISSN 1424-9286. - 73:1(2005), pp. 221-236. [10.1007/s00032-005-0045-x]
Uniqueness of positive solutions of semilinear elliptic equations and related eigenvalue problems
PACELLA, Filomena
2005
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.