Oscillation behaviors of differential and difference equations

ABSTRACTM. Sc ThesisSait SÜMÜRKENAfyon Kocatepe UniversityGraduate School of Natural and Applied SciencesDepartment of MathematicsSupervisor: Associate Professor Özkan ÖCALANDifferential equations has been studied for a long time and its application isavaliable in many scientific branches. However discontinuity cases in differentialequations are recently coped with using difference equations. So, the charecteristics ofdifferential and difference equations? solutions have a significant importance. In the firstchapter the history of those studies, oscillation of differencial and difference equations,have been dealt with and in the second chapter basic concepts, necessary theorems andlemmas have been explained. In the third chapter the conditions for oscillation ofnx' ( t ) + px ( t − τ ) = 0 , x' ( t ) + ∑ pi x ( t − τ i ) = 0 , x' ( t ) + p ( t ) x ( t − τ ) = 0i =1differential equations have been examined and in the fourth chapter oscillation ofman +1 − an + pan − k = 0 , a n+1 − a n + ∑ pi a n−ki = 0 , an +1 − an + pn an − k = 0i =1difference equations, which are the discrete analog of differencial equations, have beenexamined.2007 , 55 sayfaKey Words : Differential equation, Difference equation, Oscillationiv