| Popis: |
In this paper, we are concerned with the following modified Schrödinger equation $ \begin{array}{l} -\Delta u+V(|x|)u-\kappa u\Delta(u^2)+ \\ \qquad\qquad\qquad q\frac{h^2(|x|)}{|x|^2}(1+\kappa u^2)u\ + q\left(\int_{|x|}^{+\infty}\frac{h(s)}{s}(2+\kappa u^2(s))u^2(s){\rm{d}}s\right) u = (I_\alpha\ast F(u))f(u), \, \, x\in {\mathbb R}^2, \end{array} $ where $ \kappa $, $ q > 0 $, $ I_\alpha $ is a Riesz potential, $ \alpha\in (0, 2) $ and $ V \in \mathcal{C}({\mathbb R}^2, {\mathbb R}) $, $ F(t) = \int^t_0f(s){\rm{d}}s $. Under appropriate assumptions on $ f $ and $ V(x) $, by using the variational methods, we establish the existence of ground state solutions of the above equation. |
