The objective of this project is to investigate de dynamics defined by retarded functional differential equations (we write) RFDEs) with impulse action. We search for results on the existence and properties of periodic solutions to these equations. At first, we will study and establish conditions so that a certain RFDE which is subject to impulse effects admits a non-trivial periodic solution. Then we will consider a certain differential system which dos not have periodic solutions and we will look for conditions so that, under appropriate controls (impulses), the new system admits periodic solutions. Finallly, we will investigate the asymptotic stability of periodic solutions of impulsive RFDEs.One method we may employ to get the results is the theory of generalized ordinary differential equations and its techniques. a very general class of these equations admit a one-to-one correspondence with impulsive RFDEs. Another method we will use is the degree theory. We will consider differential-difference equations as well as differential equations with distributed delays. We are coing to consider pre-assigned moments of impulse effects where the applications accur mainly in pharmacokinetics, medicine, chemical technology, among others.
News published in Agência FAPESP Newsletter about the scholarship: