We study the existence and the profile of sign-changing solutions to the slightly subcritical problem -Δu = |u|^{2*-2-ε}u in ℬ, u = 0 on ∂ℬ, where ℬ is the unit ball in R^N, N ≥ 3, 2* = 2N/(N - 2) and ε > 0 is a small parameter. Using a Lyapunov-Schmidt reduction, we discover two new nonradial solutions having three bubbles with different nodal structures. An interesting feature is that the solutions are obtained as a local minimum and a local saddle point of a reduced function, hence they do not have a global min-max description.
Bartsch, T., D'Aprile, T.c., Pistoia, A. (2013). On the profile of sign-changing solutions of an almost critical problem in the ball. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 45(6), 1246-1258 [10.1112/blms/bdt061].
On the profile of sign-changing solutions of an almost critical problem in the ball
D'APRILE, TERESA CARMEN;
2013-01-01
Abstract
We study the existence and the profile of sign-changing solutions to the slightly subcritical problem -Δu = |u|^{2*-2-ε}u in ℬ, u = 0 on ∂ℬ, where ℬ is the unit ball in R^N, N ≥ 3, 2* = 2N/(N - 2) and ε > 0 is a small parameter. Using a Lyapunov-Schmidt reduction, we discover two new nonradial solutions having three bubbles with different nodal structures. An interesting feature is that the solutions are obtained as a local minimum and a local saddle point of a reduced function, hence they do not have a global min-max description.| File | Dimensione | Formato | |
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