| Abstract: |
| In this paper, we are concerned with the existence and asymptotic behavior of ground state in the whole space $\mathbb{R}^3$ for quasilinear Schr\odinger-Poisson systems
$$
\left\{
\begin{array}{lll}
-\Delta
u+u+K(x)\phi(x)u=a(x)f(u),\ & \ x\in \mathbb{R}^3, \
-\mbox{div}[(1+\varepsilon^4|\nabla\phi|^2)\nabla\phi]=K(x)u^2,\ & x\in \mathbb{R}^3,
\end{array}
\right.
$$
where $f(t)$ is asymptotically linear with respect to $t$ at infinity.
Under appropriate assumptions on $K,\ a$ and $ f$, we establish existence of a ground state solution $(u_\varepsilon, \phi_{\varepsilon, K}(u_\varepsilon))$ of the above system. Furthermore, for all $\varepsilon$ sufficiently small, we show that $(u_\varepsilon, \phi_{\varepsilon, K}(u_\varepsilon))$ converges to $(u_0, \phi_{0, K}(u_0))$ which is the solution of the corresponding system for $\varepsilon=0$. |
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