Existence and concentration of positive ground states for Schrodinger-Poisson equations with competing potential functions

This article concerns the Schrodinger-Poisson equation -ε²Δ u+V(x)u+K(x)φ u=P(x)|u|ᵖ⁻¹u+Q(x) |u|q-1u, x³, -ε²Δ φ=K(x)u², x³, where \(3 0\), the equation has a ground state solution. The methods used here are based on the Nehari manifold and the concentration-compactness principle. Furthermore, for ε>0 small, these ground states concentrate at a global minimum point of the least energy function. For more information see https://ejde.math.txstate.edu/Volumes/2020/78/abstr.html