Resumen de Ground State Sign-Changing Solutions for a Schrödinger–Poisson System with Steep Potential Well and Critical Growth

Xiao Qing Huang, Jia Feng Liao, Rui Qi Liu

• In this article, we consider the existence of ground state sign-changing solutions to a class of Schrödinger–Poisson systems −u + Vλ(x)u + φu = |u| 4u + μ f (u), in R3, −φ = u2, in R3, where μ > 0 and Vλ(x) = λV(x) + 1 with λ > 0. Under suitable conditions on f and V, by using the constraint variational method and quantitative deformation lemma, we prove that the above problem has one ground state sign-changing solution and the energy of ground state sign-changing solution is strictly more than twice the energy of the ground state solution. Furthermore, we also study the asymptotic behavior of ground state sign-changing solutions as λ → ∞.