Resumen de Existence and Concentration of Ground State Solutions for a Schrödinger–Poisson-Type System with Steep Potential Well

Jianwen Huang, Chunfang Chen, Chenggui Yuan

• In this paper, we study the following nonlocal problem in R3 −u + (1 + λV(x))u − μφu = f (x, u), in R3, −φ = u2, in R3, where λ > 0 is a real parameter and μ > 0 is small enough. Under some suitable assumptions on V(x) and f (x, u), we prove the existence of ground state solutions for the problem when λ is large enough via variational methods. In addition, the concentration behavior of these ground state solutions is also investigated as λ → +∞.