摘要：In this paper, we study the following Schrödinger-Kirchhoff-type equations: { − ( a + b ∫ R 3 ∇ u 2 d x ) △ u + u = k ( x ) u 2 ∗ − 2 u + μ h ( x ) u in R 3 , u ∈ H 1 ( R 3 ) , $$ \textstyle\begin{cases}-(a+b\int_{\mathrm{R}^"} \nabla u ^,\,dx)\triangle u+u= k(x) u ^{2^{*}-2}u+\mu h(x)u \quad\mbox{in } \mathrm{R}^",\\ u\in H^)(\mathrm{R}^"), \end{cases} $$ where a , b , μ > 0 $a, b,\mu>0$ are constants, 2 ∗ = 6 $2^{*}=6$ is the critical Sobolev exponent in three spatial dimensions. Under appropriate assumptions on nonnegative functions k ( x ) $k(x)$ and h ( x ) $h(x)$ , we establish the existence of positive and sign-changing solutions by variational methods.
