We study the following system of equations known as Schrödinger–Poisson problem (Formula Presented) where ϵ>0 is a small parameter, f:R→R is given, N ≥ 3 , aN is the surface measure of the unit sphere in RN and the unknowns are υ,ϕ:RN→R. We construct non-radial sign-changing multi-peak solutions in the semiclassical limit. The peaks are displaced in suitable symmetric configurations and collapse to the same point as ϵ→ 0. The proof is based on the Lyapunov–Schmidt reduction.
Non-radial sign-changing solutions for the Schrödinger–Poisson problem in the semiclassical limit
Vaira G.
2015-01-01
Abstract
We study the following system of equations known as Schrödinger–Poisson problem (Formula Presented) where ϵ>0 is a small parameter, f:R→R is given, N ≥ 3 , aN is the surface measure of the unit sphere in RN and the unknowns are υ,ϕ:RN→R. We construct non-radial sign-changing multi-peak solutions in the semiclassical limit. The peaks are displaced in suitable symmetric configurations and collapse to the same point as ϵ→ 0. The proof is based on the Lyapunov–Schmidt reduction.File in questo prodotto:
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