Positive and nodal solutions for a nonlinear Schrödinger–Poisson system with sign-changing potentials. (February 2018) - Batista, Alex M.; Furtado, Marcelo F.
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.