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