  In this paper, we are concerned with static Schr\"{o}dinger-Hartree and
Schr\"{o}dinger-Maxwell equations with combined nonlinearities. We derive the
explicit forms for positive solution $u$ in the critical case and non-existence
of nontrivial nonnegative solutions in the subcritical cases (see Theorem
\ref{Thm0} and \ref{Thm1}). The arguments used in our proof is a variant (for
nonlocal nonlinearity) of the direct moving spheres method for fractional
Laplacians in \cite{CLZ}. The main ingredients are the variants (for nonlocal
nonlinearity) of the maximum principles, i.e., \emph{Narrow region principle}
(Theorem \ref{Thm2} and \ref{Thm3}).
