Existence and concentration of nontrivial nonnegative ground state solutions to Kirchhoff-type system with Hartree-type nonlinearity

Abstract

A Kirchhoff-type fractional elliptic system with Hartree-type nonlinearity is proposed to provide a unified framework for well-known nonlinear Schrodinger equations, Kirchhoff equations and Schrodinger–Poisson systems. The existence of nontrivial nonnegative ground state solutions to the system is proved when the coefficient of the potential function is larger than a threshold value, and a precise estimate of the threshold value is given for a prototypical example. It is also shown that the ground state solution concentrates on the zero set of the potential function when the coefficient tends to infinity.