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 [10.1017/S0308210507000212].

Linear instability of entire solutions for a class of non-autonomous elliptic equations

ESPOSITO, PIERPAOLO
2008-01-01

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.
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 [10.1017/S0308210507000212].
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/118228
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 12
  • ???jsp.display-item.citation.isi??? 12
social impact