Resumen de Ground State Solution of Kirchhoff Problems with Hartree Type Nonlinearity

Linjie Wang, Haidong Liu

• For the Kirchhoff type equation − a + b R3 |∇u| 2 dx u + V(x)u = (Iα ∗ |u| p)|u| p−2u in R3, where a, b > 0, 0 <α< 3, 2 < p < 3+α and Iα is the Riesz potential, we establish the existence of a positive ground state solution by using Nehari manifold technique and concentration compactness argument. The main novelty in our context is that the potential V exhibits a mixed behavior, i.e., V is periodic in some directions while tends to a positive constant in the remaining ones.