Yüksek basamaktan fark denklemlerinin çözümlerinin salınımlılığı
Özet
ABSTRACT Ph. D. Thesis OSCILLATORY BEHAVIOUR OF SOLUTIONS OF HIGHER ORDER DIFFERENCE EQUATIONS Yaşar BOLAT Graduate School of Natural and Applied Sciences Department of Mathematics Supervisor : Prof. Dr. Ömer AKIN Our first aim in this thesis is to give some information about the solutions of given difference equation i.e. to search a qualitative investigation. In recent years, works on the oscillation theory have increased in importance. The majority of these works are based on the nonlinear difference equations and neutral difference equations which have many applications in economy, health, social and technical sciences. This situation has taken us to examine these types of equations. In this thesis, nonlinear neutral type homogenous and nonhomegenous functional difference equations and difference equation with delay term are considered and oscillatory behaviour of solutions of these difference equations are investigated. This thesis is consist of four chapters. First chapter is introduction chapter of the thesis. In this chapter, we gave some information about a short history of difference equations, a short explanation about results in the earlier works which are similar to the considered difference equations in the thesis and a short information about that results in the thesis obtained. The second chapter is consist of some fundamental notions which related with the difference equations and oscillatory behaviour of them and some auxiliary theorems. In the third and fourth chapters we gave new results concerning the oscillatory behaviour of solutions of the considered difference equations. In the appendix, we gave some our papers which include some results that given third and fourth chapter. 2003, 49 page Key Words: Difference equation, nonlinear difference equation, higher order difference equation, neutral difference equation, oscillatory solution, nonoscfllatory solution, osculating coefficients.