In this paper we are concerned with the following Neumann problem where ϵ is a small positive parameter, f is an odd superlinear and subcritical nonlinearity, Ω is a bounded 4 domain in N without any symmetry assumption. Denoting by (P), P ∂Ω, the mean curvature of the boundary, it is known that this problem has positive multiple boundary peak solutions with each peak concentrating at a different critical point of or with all the peaks approaching a local minimum point of . In this paper we assume that has a nondegenerate maximum point P 0 ∂Ω and we show that there exists a ℓ-peak solution with mixed positive and negative peaks concentrating at P 0.
D'Aprile, T.c., Pistoia, A. (2010). Nodal clustered solutions for some singularly perturbed Neumann problems. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 35(8), 1355-1401 [10.1080/03605302.2010.490284].
Nodal clustered solutions for some singularly perturbed Neumann problems
D'APRILE, TERESA CARMEN;
2010-01-01
Abstract
In this paper we are concerned with the following Neumann problem where ϵ is a small positive parameter, f is an odd superlinear and subcritical nonlinearity, Ω is a bounded 4 domain in N without any symmetry assumption. Denoting by (P), P ∂Ω, the mean curvature of the boundary, it is known that this problem has positive multiple boundary peak solutions with each peak concentrating at a different critical point of or with all the peaks approaching a local minimum point of . In this paper we assume that has a nondegenerate maximum point P 0 ∂Ω and we show that there exists a ℓ-peak solution with mixed positive and negative peaks concentrating at P 0.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.