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The Poynting-Robertson(P-R) effect on Lyapunov stability of equilibriumpoints is being discussed in the the generalized photogravitational Chermnykh'sproblem when bigger primary is a sours of radiation and smaller primary is anoblate spheriod. We derived the equations of motion, obtained the equilibriumpoints and examined the linear stability of the equilibrium points for variousvalues of parameter which have been used in the present problem. We haveexamined the effect of gravitational potential from the belt. The positions ofthe equilibrium points are different from the position in classical case. Wehave seen that due to the P-R effect all the equilibrium points are unstable inLyapunov sense.

Poynting-Robertson Effect on the Lyapunov Stability of Equilibrium Points in the Generalized Photogravitational Chermnykh's Problem