Existence of equilibrium points and their linear stability in the generalized photogravitational Chermnykh-like problem with power-law profile

We consider the modified restricted three body problem with power-law density profile of disk, which rotates around the center of mass of the system with perturbed mean motion. Using analytical and numerical methods, we have found equilibrium points and examined their linear stability. We have also found the zero velocity surface for the present model. In addition to five equilibrium points there exists a new equilibrium point on the line joining the two primaries. It is found that L (1) and L (3) are stable for some values of inner and outer radius of the disk while other collinear points are unstable, but L (4) is conditionally stable for mass ratio less than that of Routh's critical value. Lastly, we have studied the effects of radiation pressure, oblateness and mass of the disk on the motion and stability of equilibrium points.