We prove the existence of solutions for the singularly perturbed Schrödinger-Newton system {(h{stroke}2 Δ ψ - V (x) ψ + U ψ = 0; h{stroke}2 Δ U + 4 π γ | ψ |2 = 0) in R3 with an electric potential V that decays polynomially fast at infinity. The solution ψ concentrates, as h{stroke} → 0, around (structurally stable) critical points of the electric potential. As a particular case, isolated strict extrema of V are allowed. © 2010 Elsevier Ltd. All rights reserved.
Secchi, S. (2010). A note on Schrödinger-Newton systems with decaying electric potential. NONLINEAR ANALYSIS, 72(9-10), 3842-3856 [10.1016/j.na.2010.01.021].
A note on Schrödinger-Newton systems with decaying electric potential
SECCHI, SIMONE
2010
Abstract
We prove the existence of solutions for the singularly perturbed Schrödinger-Newton system {(h{stroke}2 Δ ψ - V (x) ψ + U ψ = 0; h{stroke}2 Δ U + 4 π γ | ψ |2 = 0) in R3 with an electric potential V that decays polynomially fast at infinity. The solution ψ concentrates, as h{stroke} → 0, around (structurally stable) critical points of the electric potential. As a particular case, isolated strict extrema of V are allowed. © 2010 Elsevier Ltd. All rights reserved.
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