n this paper we consider the problem −Δu+u=up on a bounded domain with a homogeneous Neumann boundary condition. We prove the existence of a one-spike solution to (0.1) which concentrates around a topologically non trivial critical point of the mean curvature of the boundary with positive value. Under some symmetry assumption on Ω, namely if Ω is even with respect to N−1 variables and 0∈∂Ω is a point with positive mean curvature, we prove existence of solutions to (0.1) which resemble the form of a super-position of spikes centered at 0.
Super position of bubbles in a slightly supercritical Neumann problem / DEL PINO, M.; Musso, M.; Pistoia, Angela. - In: ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE. - ISSN 0294-1449. - STAMPA. - 22(2005), pp. 45-82. [10.1016/j.anihpc.2004.05.001]
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Titolo: | Super position of bubbles in a slightly supercritical Neumann problem | |
Autori: | ||
Data di pubblicazione: | 2005 | |
Rivista: | ||
Citazione: | Super position of bubbles in a slightly supercritical Neumann problem / DEL PINO, M.; Musso, M.; Pistoia, Angela. - In: ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE. - ISSN 0294-1449. - STAMPA. - 22(2005), pp. 45-82. [10.1016/j.anihpc.2004.05.001] | |
Handle: | http://hdl.handle.net/11573/50174 | |
Appartiene alla tipologia: | 01a Articolo in rivista |