摘要 : This article is dedicated to the following Kirchhoff-type problem with Hartree-type nonlinearity: I-(epsilon(2)a + epsilon b f (R)3 |& nabla;u|(2)dx).A.u + V (x)u=epsilon(mu-3) K(x)(W mu(x) & lowast; |u|(p))|u|(p-2)u, u is an elem... 展开 This article is dedicated to the following Kirchhoff-type problem with Hartree-type nonlinearity: I-(epsilon(2)a + epsilon b f (R)3 |& nabla;u|(2)dx).A.u + V (x)u=epsilon(mu-3) K(x)(W mu(x) & lowast; |u|(p))|u|(p-2)u, u is an element of H-1(R-3), where a, b > 0 are constants, epsilon > 0 is a parameter, 0 < mu < 3, p is an element of [2, 6 - mu), W mu(x) is convolution kernel, V(x) is nonnegative continuous external potential and K(x) is an element of C-1(R-3). Under some suitable assumptions on V(x) and K(x), we prove the existence and concentration of a positive ground state solution as epsilon -> 0 via Pohoz?aev- Nehari manifold method. If K(x) is a positive constant, as its supplementary results, we also obtain the nonexistence of nontrivial solutions for p > 6 - mu. 收起