Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Table of Contents - 2008 - Volume 138, Issue 05  

Research Article

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

Pierpaolo Espositoa1

a1 Dipartimento di Matematica, Università degli Studi ‘Roma Tre’, Largo San Leonardo Murialdo 1, 00146 Roma, Italy (esposito@mat.uniroma3.it).

We study the effect of the potential |y|α on the stability of entire solutions for elliptic equations on xs211DN, 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.

(Received February 19 2007)

(Accepted July 20 2007)