Positive and nodal solutions for a nonlinear Schrödinger–Poisson system with sign-changing potentials. (February 2018)

• Record Type: Journal Article
• Authors: Batista, Alex M.; Furtado, Marcelo F.
• Is Part Of: Nonlinear analysis. Volume 39(2018)
• Page Start: 142
• Page End: 156
• Publication Date: 2018-02
• Subjects: Schrödinger–Poisson system -- Positive solution -- Nodal solution; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2017.06.005
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We use a variational approach to deal with the system − Δ u + V ( x ) u + K ( x ) ϕ u = a ( x ) | u | p − 1 u, − Δ ϕ = K ( x ) u 2, x ∈ R 3, with 3 < p < 5 . Under some mild conditions on the sign-changing potentials V and a we obtain two nonzero solutions. One of them is nonnegative and the other one changes sign.