  Motivated by importance of the existence of quark matter on structure of
neutron star. For this purpose, we use a suitable equation of state (EoS) which
include three different parts: i) a layer of hadronic matter, ii) a mixed phase
of quarks and hadrons, and, iii) a strange quark matter in the core. For this
system, in order to do more investigation of the EoS, we evaluate energy, Le
Chatelier's principle and stability conditions. Our results show that the EoS
satisfies these conditions. Considering this EoS, we study the effect of quark
matter on the structure of neutron stars such as maximum mass and the
corresponding radius, average density, compactness, Kretschmann scalar,
Schwarzschild radius, gravitational redshift and dynamical stability. Also,
considering the mentioned EoS in this paper, we find that the maximum mass of
hybrid stars is a little smaller than that of the corresponding pure neutron
star. Indeed the maximum mass of hybrid stars can be quite close to the pure
neutron stars. Our calculations about the dynamical stability show that these
stars are stable against the radial adiabatic infinitesimal perturbations. In
addition, our analyze indicates that neutron stars are under a contraction due
to the existence of quark core.
