In this paper. we prove that the Brezis-Nirenberg problem with slightly supercritical non-linearity. [GRAPHICS] where Omega is any bounded smooth domain in R(N), N >= 5, and lambda is a positive number. has two solutions with the shape of a tower of bubbles. for all epsilon > 0 sufficiently small. We also prove that the slightly subcritical problem: [GRAPHICS] where Omega is any bounded smooth domain in R(N), N >= 3, has a solution with the shape of a tower of sign changing bubbles, for all epsilon > 0 sufficiently small. (C) 2009 Elsevier Masson SAS. All rights reserved.
Tower of bubbles for almost critical problems in general domains / Monica, Musso; Pistoia, Angela. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - STAMPA. - 93:1(2010), pp. 1-40. [10.1016/j.matpur.2009.08.001]
Tower of bubbles for almost critical problems in general domains
PISTOIA, Angela
2010
Abstract
In this paper. we prove that the Brezis-Nirenberg problem with slightly supercritical non-linearity. [GRAPHICS] where Omega is any bounded smooth domain in R(N), N >= 5, and lambda is a positive number. has two solutions with the shape of a tower of bubbles. for all epsilon > 0 sufficiently small. We also prove that the slightly subcritical problem: [GRAPHICS] where Omega is any bounded smooth domain in R(N), N >= 3, has a solution with the shape of a tower of sign changing bubbles, for all epsilon > 0 sufficiently small. (C) 2009 Elsevier Masson SAS. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
