(untitled) (Journal of Nonlinear Modeling and Analysis, 2024)
In this paper, we consider the following Schrödinger-Poisson system with a cubic term align*0.10.1 cases -Δ u+V(|x|)u+λφ u=|u|^2u in R^3, -Δφ=u^2 in R^3, cases align* where λ > 0 and the radial function V (x) is an external potential. By taking advantage of the Gersgorin disc theorem and Miranda theorem, via the variational method and blow up analysis, we prove that for each positive integer k, problem (0.1) admits a radial nodal solution U^λ_k,4 that changes sign exactly k times. Furthermore, the energy of U^λ_k,4 is strictly increasing in k and the asymptotic behavior of U^λ_k,4 as λ → 0_+ is established. These results extend the existing ones from the super-cubic case in [17] to the cubic case.