We examine the stability of { AdS } _ { p } \times { S } ^ { n } \times { S } ^ { q - n } .
The initial data constructed by De Wolfe et al ( ( 1 ) ) has been carefully analyised and we have confirmed that there is no lower bound for the total mass for q < 9 .
The effective action on { AdS } _ { p } has been derived for dilatonic compactification of the system to describe the non-linear fluctuation of the background space-time .
The stability is discussed applying the positive energy theorem to the effective theory on AdS , which again shows the stability for q \geq 9 .