  The observations of optical and near-infrared counterparts of binary neutron
star mergers not only enrich our knowledge about the abundance of heavy
elements in the Universe, or help reveal the remnant object just after the
merger as generally known, but also can effectively constrain dense nuclear
matter properties and the equation of state (EOS) in the interior of the
merging stars. Following the relativistic mean-field description of nuclear
matter, we perform the Bayesian inference of the EOS and the nuclear matter
properties using the first multi-messenger event GW170817/AT2017gfo, together
with the NICER mass-radius measurements of pulsars. The kilonova is described
by a radiation-transfer model with the dynamical ejecta, and light curves
connect with the EOS through the quasi-universal relations between the ejecta
properties (the ejected mass, velocity, opacity or electron fraction) and
binary parameters (the mass ratio and reduced tidal deformability). It is found
that the posterior distributions of the reduced tidal deformability from the
AT2017gfo analysis display a bimodal structure, with the first peak enhanced by
the GW170817 data, leading to slightly softened posterior EOSs, while the
second peak cannot be achieved by a nuclear EOS with saturation properties in
their empirical ranges. The inclusion of NICER data in our analyses results in
stiffened EOS posterior because of the massive pulsar PSR J0740+6620. We give
results at nuclear saturation density for the nuclear incompressibility, the
symmetry energy and its slope, as well as the nucleon effective mass, from our
analysis of those observational data.
