caa a22 4500 60619424X CHVBK 20210128100913.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s00030-014-0303-0 doi (NATIONALLICENCE)springer-10.1007/s00030-014-0303-0 Non-radial sign-changing solutions for the Schrödinger-Poisson problem in the semiclassical limit [Elektronische Daten] [Isabella Ianni, Giusi Vaira] We study the following system of equations known as Schrödinger-Poisson problem $${\left\{\begin{array}{ll}-\epsilon^2\Delta \upsilon + \upsilon +\phi \upsilon=f(\upsilon)&\quad\mbox{in}\mathbb R^N\\-\Delta\phi =a_N \upsilon^2 &\quad \mbox{in} \mathbb R^N\\\phi\rightarrow 0 &\quad\mbox{as} |x|\rightarrow +\infty\end{array}\right.}$$ - ϵ 2 Δ υ + υ + ϕ υ = f ( υ ) in R N - Δ ϕ = a N υ 2 in R N ϕ → 0 as | x | → + ∞ where $${{{\epsilon > 0}}}$$ ϵ > 0 is a small parameter, $${{{f{:}\;\mathbb{R}\rightarrow\mathbb{R}}}}$$ f : R → R is given, N≥ 3 , a N is the surface measure of the unit sphere in $${{{\mathbb{R}^{N}}}}$$ R N and the unknowns are $${{{\upsilon, \phi{:}\;\mathbb{R}^{N}\rightarrow\mathbb{R}}}}$$ υ , ϕ : R N → 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 $${{{\epsilon}}}$$ ϵ → 0. The proof is based on the Lyapunov-Schmidt reduction. Springer Basel, 2014 Schrödinger-Poisson problem nationallicence Semiclassical limit nationallicence Cluster solutions nationallicence Sign-changing solutions nationallicence Variational methods nationallicence Lyapunov-Schmidt reduction nationallicence Ianni Isabella Dipartimento di Matematica e Fisica, Seconda Università degli Studi di Napoli, viale Lincoln 5, 81100, Caserta, Italy aut Vaira Giusi sezione di Matematica, Dipartimento di Scienze di Base e Applicate per l'Ingegneria, Università La Sapienza di Roma, Via A. Scarpa 14, 00185, Rome, Italy aut Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/4(2015-08-01), 741-776 1021-9722 22:4<741 2015 22 30 https://doi.org/10.1007/s00030-014-0303-0 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00030-014-0303-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ianni Isabella Dipartimento di Matematica e Fisica, Seconda Università degli Studi di Napoli, viale Lincoln 5, 81100, Caserta, Italy aut NATIONALLICENCE 700 1- Vaira Giusi sezione di Matematica, Dipartimento di Scienze di Base e Applicate per l'Ingegneria, Università La Sapienza di Roma, Via A. Scarpa 14, 00185, Rome, Italy aut NATIONALLICENCE 773 0- Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/4(2015-08-01), 741-776 1021-9722 22:4<741 2015 22 30