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]
Super position of bubbles in a slightly supercritical Neumann problem
PISTOIA, Angela
2005
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
