EXISTENCE OF PERIODIC SOLUTIONS OF SECOND-ORDER NONLINEAR INTEGRO-DIFFERENTIAL EQUATIONS WITH VARIABLE DELAY

In this work, we use fixed point theorems and choose available operators to prove the existence of periodic solutions of a second-order nonlinear delay integro-differential equations (1). During the process Eq (1) is converted into an equivalent integral equation but with the same properties from which appropriate mappings are constructed. We offer existence criteria based on sufficient conditions on f, p, q to conclude existence of periodic solutions.