# Asymptotic Behavior of Solutions to Nonlinear Neutral Differential Equations

## EMU I-REP

 dc.contributor.author Hasanbulli, Mustafa dc.date.accessioned 2012-11-30T13:14:43Z dc.date.available 2012-11-30T13:14:43Z dc.date.issued 2010 dc.identifier.citation Hasanbulli, Mustafa. (2010). Asymptotic Behavior of Solutions to Nonlinear Neutral Differential Equations. Thesis (Ph.D.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus. en_US dc.identifier.uri http://hdl.handle.net/11129/93 dc.description Doctor of Philosophy in Mathematics. Thesis (Ph.D.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2010. Supervisor: Assoc. Prof. Dr. Svitlana Rogovchenko. en_US dc.description.abstract In Chapter 2 of this thesis, in the first part, we deal with asymptotic behavior of nonoscillatory solutions to higher order nonlinear neutral differential equations of the form (x (t) + p (t) x (t − τ ))(n) + f (t, x (t) , x (ρ (t)) , x (t) , x (σ (t))) = 0,for n ≥ 2. We formulate sufficient conditions for all non-oscillatory solutions to behave like polynomial functions at infinity. For the higher order differential equation (x (t) + p (t) x (t − τ ))(n) + f (t, x (t) , x (ρ (t))) = 0, we provide necessary and sufficient conditions that guarantee existence of non-oscillatory en_US solutions with polynomial-like behavior at infinity. In Chapter 3, we look into oscillation problem of second order nonlinear neutral differential equations r (t) ψ (x (t)) (x (t) + p (t) x (τ (t))) + q (t) f (x (t) , x (σ (t))) = 0 and r (t) (x (t) + p (t) x (τ (t))) + q (t) f (x (t) , x (σ (t))) = 0. dc.language.iso en en_US dc.publisher Eastern Mediterranean University (EMU) en_US dc.subject Mathematics en_US dc.subject Asymptotic Behavior - Oscillation - Positive Solutions - Neutral Equations en_US dc.title Asymptotic Behavior of Solutions to Nonlinear Neutral Differential Equations en_US dc.type Thesis en_US
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