@article{article_101372, title={SEPARATE CONTRACTION AND EXISTENCE OF PERIODIC SOLUTIONS IN TOTALLY NONLINEAR DELAY DIFFERENTIAL EQUATIONS}, journal={Hacettepe Journal of Mathematics and Statistics}, volume={41}, pages={1–13}, year={2012}, author={Adıvar, Murat and Islam, Muhammad N. and Raffoul, Youssef N.}, keywords={Krasnoselskii’s fixed point theorem,Large contraction,Periodic solution,Positive periodic solution,Separate contraction,Totally nonlinear delay differential equations}, abstract={In this study, we employ the fixed point theorem of Krasnoselskii and <br />the concepts of separate and large contractions to show the existence <br />of a periodic solution of a highly nonlinear delay differential equation. <br />Also, we give a classification theorem providing sufficient conditions for <br />an operator to be a large contraction, and hence, a separate contraction. <br />Finally, under slightly different conditions, we obtain the existence of <br />a positive periodic solution.}, number={1}, publisher={Hacettepe University}