On a planar Hartree-Fock type system involving the (2,q)-Laplacian in the zero mass case

Abstract

In this work, we study a class of planar Hartree-Fock type system involving the Laplacian operator. Due to the nature of the problem, we deal with the logarithmic integral kernel. We introduce a suitable function space to study the system variationally. It is established existence of positive vector ground state solutions. In addition, we study the asymptotic behavior of the solutions and we also provide a nonexistence result. Our approach is based on Nehari method and Moser iteration scheme.