We study the effect of the potential |y|^α on the stability of entire solutions for elliptic equations on R^N, N\geq 2, with exponential or smoooth/singular polynomial nonlinearities. Instability properties are crucial in order to establish regularity of the extremal solution to some related Dirichlet nonlinear eigenvalue problem on bounded domains. As a by-product of our results, we will improve the known results about the regularity of such solutions.
ESPOSITO P (2008). Linear instability of entire solutions for a class of non-autonomous elliptic equations. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SECTION A. MATHEMATICS, 138(5), 1005-1018.
Titolo: | Linear instability of entire solutions for a class of non-autonomous elliptic equations |
Autori: | |
Data di pubblicazione: | 2008 |
Rivista: | |
Citazione: | ESPOSITO P (2008). Linear instability of entire solutions for a class of non-autonomous elliptic equations. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SECTION A. MATHEMATICS, 138(5), 1005-1018. |
Abstract: | We study the effect of the potential |y|^α on the stability of entire solutions for elliptic equations on R^N, N\geq 2, with exponential or smoooth/singular polynomial nonlinearities. Instability properties are crucial in order to establish regularity of the extremal solution to some related Dirichlet nonlinear eigenvalue problem on bounded domains. As a by-product of our results, we will improve the known results about the regularity of such solutions. |
Handle: | http://hdl.handle.net/11590/118228 |
Appare nelle tipologie: | 1.1 Articolo in rivista |