Existence and asymptotic behaviour of ground state solutions for quasilinear Schrodinger-Poisson systems in $R^3$
Existence and asymptotic behaviour of ground state solutions for quasilinear Schrodinger-Poisson systems in $R^3$
In this paper, we are concerned with existence and asymptotic behavior of ground state in the whole space $\mathbb{R}^3$ for quasilinear Schr\"odinger--Poisson systems $$ \begin{cases} -\Delta u+u+K(x)\phi(x)u=a(x)f(u), x\in \mathbb{R}^3, \\ -\mbox{div}[(1+\varepsilon^4|\nabla\phi|^2)\nabla\phi]=K(x)u^2, x\in \mathbb{R}^3, \end{cases} $$ when the nonlinearity coefficient $\varepsilon\ge 0$ goes to zero, where $f(t)$ is asymptotically linear with …