We consider the supercritical problem -Delta u = vertical bar u vertical bar(p-1)u in D, u = 0 on partial derivative D, where D is a bounded smooth domain in RN and p is smaller than the kappa-th critical Sobolev exponent 2*(N,kappa) := N-kappa+2/N-kappa-2 with 1 <= kappa <= N - 3. We show that in some suitable torus-like domains D there exists an arbitrary large number of sign-changing solutions with alternate positive and negative layers which concentrate at different rates along a kappa-dimensional submanifold of partial derivative D as p approaches 2*(N,kappa) from below. (C) 2013 Elsevier Inc. All rights reserved.
Boundary towers of layers for some supercritical problems / Seunghyeok, Kim; Pistoia, Angela. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 255:8(2013), pp. 2302-2339. [10.1016/j.jde.2013.06.017]
Boundary towers of layers for some supercritical problems
PISTOIA, Angela
2013
Abstract
We consider the supercritical problem -Delta u = vertical bar u vertical bar(p-1)u in D, u = 0 on partial derivative D, where D is a bounded smooth domain in RN and p is smaller than the kappa-th critical Sobolev exponent 2*(N,kappa) := N-kappa+2/N-kappa-2 with 1 <= kappa <= N - 3. We show that in some suitable torus-like domains D there exists an arbitrary large number of sign-changing solutions with alternate positive and negative layers which concentrate at different rates along a kappa-dimensional submanifold of partial derivative D as p approaches 2*(N,kappa) from below. (C) 2013 Elsevier Inc. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
