On the Lp Gaussian Minkowski problem

Existence of symmetric (resp. asymmetric) solutions to the $L_p$ Gaussian Minkowski problem for $p\le 0$ (resp. $p\ge 1$) will be provided. Moreover, existence and uniqueness of smooth solutions to the problem for $p>n$ will also be proved without the restriction that the Gaussian volumes of convex bodies are not less than one-second.