The response to antiangiogenic anticancer drugs that inhibit endothelial cell proliferation

In the first part of this paper we study the properties of a class of linear differential equations with periodic real coefficients and show that the structure of this family of systems guarantees the unstability of the null solution. In the second part, we use this property to demonstrate that antiangiogenic drugs that act only inhibiting the endothelial cell proliferation might be uneffective in tumor elimination under some relevant biological conditions. Finally, we derive some sufficient criteria that guarantee the disease elimination by therapies using this class of drugs.