EXISTENCE OF NONTRIVIAL SOLUTIONS AND SIGN-CHANGING SOLUTIONS TO NONLOCAL KIRCHHOFF EQUATION WITH THE TERNI OF CHOQUARD IN RN

. In this paper, we are concerned with a class nonlocal Kirchhoff equation with the term of Choquard Z-(a + b RN |del u|2dx)triangle u + V (x)u = (I alpha & lowast; k|u|p)k(x)|u|p-2u, x is an element of RN, where a and b are positive constants. With the help of the Hardy-LittlewoodSobolev inequality, we showed the existence of the bounded convergent (PS)c sequence. Combining with the Mountain pass theorem, we proved the existence of a nontrivial solution for the class nonlocal Kirchhoff equation with the term of Choquard. Furthermore, we also obtained at least one least energy signchanging solution via the Hardy-Littlewood-Sobolev inequality and Brouwer topological degree.