Ground State Solutions to a Coupled Nonlinear Logarithmic Hartree System

Abstract

In this paper, we study the following coupled nonlinear logarithmic Hartree system

where $β,\mu_i,λ_i$ ($i=1,2$) are positive constants, ∗ denotes the convolution in $\mathbb{R}^2.$ By considering the constraint minimum problem on the Nehari manifold, we prove the existence of ground state solutions for $β > 0$ large enough. Moreover, we also show that every positive solution is radially symmetric and decays exponentially.