Abstract
We used a discrete time version of viabilitytheory in order to study the sustainable therapies againstthe cancer. We assume that the tumor is composed of twosubpopulations, one resistant and the another sensitive. Weconsider a discrete model in order to simulate the responseof this tumor to therapy, and we apply the Bellman equationwithin the viable control framework for calculating viabilitykernel, so as to determine the existence of a therapy thatmaintain the cell population bounded. Both theoretical andnumerical results are presented.