Abstract
In this paper, we study the following quasilinear Choquard equations of
the form $$\ -\Delta
u+V(x)u-\Delta
(|u|^{2\alpha})|u|^{2\alpha-2}u=(|x|^{-\mu}\ast
G(u))g(u), \ x \ \in
R^N,$$ where
$1\geq\alpha>\frac{1}{2}$,
$V \in C(\mathbb{R}^N,
\mathbb{R})$, $g \in
C(\mathbb{R}^N, \
\mathbb{R})$. Distinguished from two situations
$\lim\limits_{|x|\rightarrow\infty}V(x)=+\infty$
or
$\lim\limits_{|x|\rightarrow\infty}V(x)<+\infty$,
we research the existence of nontrivial solutions and a sequence of high
energy solutions.