We study the existence and profile of sign-changing solutions of the supercritical problem -Delta u = |u|(p-1)u in D, u = 0 on partial derivative D, where D is a smooth open bounded domain in R-n and p > 1. In particular, for suitable domains D, we prove that, for any integer m, if p is large enough, such a problem has a sign-changing solution which concentrates positively and negatively along m different (n - 2)-dimensional submanifolds of the boundary of D that collapse to a suitable submanifold of the boundary as p -> + infinity.
Clustered boundary layer sign-changing solutions for a supercritical problem / S., Kim; Pistoia, Angela. - In: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6107. - STAMPA. - 88:1(2013), pp. 227-250. [10.1112/jlms/jdt006]
Clustered boundary layer sign-changing solutions for a supercritical problem
PISTOIA, Angela
2013
Abstract
We study the existence and profile of sign-changing solutions of the supercritical problem -Delta u = |u|(p-1)u in D, u = 0 on partial derivative D, where D is a smooth open bounded domain in R-n and p > 1. In particular, for suitable domains D, we prove that, for any integer m, if p is large enough, such a problem has a sign-changing solution which concentrates positively and negatively along m different (n - 2)-dimensional submanifolds of the boundary of D that collapse to a suitable submanifold of the boundary as p -> + infinity.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.