Abstract:

In this paper, we consider the following quasilinear Schrödinger equations of Choquard type $\begin{eqnarray*} -\triangle u+\frac{k}{2}u\triangle u^2+V(x)u=(I_{\alpha}\ast|u|^{p})|u|^{p-2}u, \, \, x\in\mathbb{R}^N, \end{eqnarray*}$ where $N\geq3$, 0 < $\alpha$ < $N$, $<p<\frac{N+\alpha}{N-2}$, $I_{\alpha}$ is the Riesz potential, $V(x)$ is a positive continuous potential and $k$ is a non-negative parameter. The existence of ground state solutions is established via Pohožaev manifold approach.

Key words: Choquard type problems, Pohožaev manifold, Ground state solutions