Resumen de Ground State Solution for the Logarithmic Schrödinger–Poisson System with Critical Growth

Yaqing Cai, Yulin Zhao

• In this paper we investigate a class of logarithmic Schrödinger–Poisson system with critical growth which are from physically relevant backgrounds. Under suitable assumptions on the potential V(x), we obtain the existence of ground state solution for ε > 0 sufficiently small via using a constrained minimization on a Nehari manifold and some new techniques. Specially, by restricting the least energy c to a suitable interval, we overcome some difficulties brought by the critical term u5 for restoring the compactness of the minimizing sequence of the least energy c.