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Englishn 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.
http://hdl.handle.net/11573/50174| Titolo: | Super position of bubbles in a slightly supercritical Neumann problem |
| Autori interni: | PISTOIA, Angela |
| Data di pubblicazione: | 2005 |
| Rivista: | ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE |
| Abstract: | 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. |
| Handle: | http://hdl.handle.net/11573/50174 |
| Appare nelle tipologie: | 01.a Pubblicazione su Rivista |
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