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

摘要

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.