Ground state solutions for asymptotically periodic Schrödinger–Poisson systems involving Hartree-type nonlinearities
Ground state solutions for asymptotically periodic Schrödinger–Poisson systems involving Hartree-type nonlinearities
We use the non-Nehari manifold method to deal with the system $$ \textstyle\begin{cases} -\Delta u+V(x)u+\phi u= (\int_{\mathbb{R}^{3}}\frac {Q(y)F(u(y))}{|x-y|^{\mu}}\,dy )Q(x)f(u(x)),\quad x\in\mathbb{R}^{3}, \\ -\Delta\phi=u^{2}, \quad u \in H^{1}(\mathbb{R}^{3}), \end{cases} $$ where $V(x)$ and $Q(x)$ are periodic and asymptotically periodic in x. Under some mild conditions on f, we establish the existence of …