Least energy radial sign-changing solution for the Schröinger-Poisson system in r3 under an asymptotically cubic nonlinearity

2018/05/01 by Edwin G. Murcia, Murcia, Edwin G., Gaetano Siciliano +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Nonlinear Partial Differential Equations #math.AP #msc:35J50 #msc:35Q60 #msc:58E30

paper · pdf · doi:10.48550/arxiv.1805.00259

arxiv created 2018/05/01 · arxiv updated 2018/05/02

Abstract

In this paper we consider the following Schrödinger-Poisson system in the whole \mathbb R³, \ -Δu+u+ λϕu=f(u) · in \mathbb R³, -Δϕ= u² · in \mathbb R³, . where λ>0 and the nonlinearity f is "asymptotically cubic" at infinity. This implies that the nonlocal term ϕu and the nonlinear term f(u) are, in some sense, in a strict competition. We show that the system admits a least energy sign-changing and radial solution obtained by minimizing the energy functional on the so-called nodal Nehari set).

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