We study the existence of sign-changing solutions with multiple bubbles to the slightly subcritical problem -Δu=|u|^{2*-2-ε}u in Ω,u=0 on ∂Ω, where Ω is a smooth bounded domain in R^N, N≥3, 2*=2N/(N-2) and ε>0 is a small parameter. In particular we prove that if Ω is convex and satisfies a certain symmetry, then a nodal four-bubble solution exists with two positive and two negative bubbles.
Bartsch, T., D'Aprile, T.c., Pistoia, A. (2013). Multi-bubble nodal solutions for slightly subcritical elliptic problems in domains with symmetries. ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE, 30(6), 1027-1047 [10.1016/j.anihpc.2013.01.001].
Multi-bubble nodal solutions for slightly subcritical elliptic problems in domains with symmetries
D'APRILE, TERESA CARMEN;
2013-01-01
Abstract
We study the existence of sign-changing solutions with multiple bubbles to the slightly subcritical problem -Δu=|u|^{2*-2-ε}u in Ω,u=0 on ∂Ω, where Ω is a smooth bounded domain in R^N, N≥3, 2*=2N/(N-2) and ε>0 is a small parameter. In particular we prove that if Ω is convex and satisfies a certain symmetry, then a nodal four-bubble solution exists with two positive and two negative bubbles.| File | Dimensione | Formato | |
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