Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-18T07:12:44.476Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  08 October 2008

Pierpaolo Esposito
Pierpaolo Esposito
Affiliation:
Dipartimento di Matematica, Università degli Studi ‘Roma Tre’, Largo San Leonardo Murialdo 1, 00146 Roma, Italy ([email protected]).
Get access Rights & Permissions [Opens in a new window]

Extract

We study the effect of the potential |y|α on the stability of entire solutions for elliptic equations on ℝN, N ≥ 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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 138 , Issue 5 , October 2008 , pp. 1005 - 1018
Copyright
Copyright © Royal Society of Edinburgh 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)