Resumen de Ground State Sign-Changing Solution for Schrödinger-Poisson System with Critical Growth

Ziheng Zhang, Ying Wang, Rong Yuan

• This article is devoted to study the nonlinear Schrödinger-Poisson system with pure power nonlinearities −u + u + φu = |u|p−1u + |u| 4u, x ∈ R3, −φ = u2, x ∈ R3, where 4 < p < 5. By employing constraint variational method and a variant of the classical deformation lemma, we show the existence of one ground state signchanging solution with precisely two nodal domains, which improves and generalizes the existing results by Wang, Zhang and Guan (J. Math. Anal. Appl. 479 (2019), 2284–2301).