Classification of nonoscillatory solutions of nonlinear neutral differential equations

Mustafa Hasanbulli; Yuri V. Rogovchenko

doi:10.3934/proc.2009.2009.340

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2009, Volume 2009: 340-348. Doi: 10.3934/proc.2009.2009.340 open access

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Classification of nonoscillatory solutions of nonlinear neutral differential equations

Mustafa Hasanbulli^1, and
Yuri V. Rogovchenko^2,

1.
Department of Mathematics, Faculty of Arts and Sciencecs, Eastern Mediterranean University, Famagusta, TRNC, Mersin 10
2.
School of Pure and Applied Natural Sceinces, University of Kalmar, SE-39182 Kalmar

Received: July 31, 2008

Revised: May 31, 2009

Published: August 2009

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Abstract

Nonoscillatory solutions of a general class of second order functional neutral differential equations of the form

$(r(t)(x(t)+p(t)x(t-\tau))')'+f(t,x(\sigma_{1}(t)),x(\sigma_{2}(t)),...,x(\sigma_{n}(t)))=0$

have been classified in accordance with their asymptotic behavior.

Keywords:

Nonlinear neutral differential equations,
nonoscillatory solutions,
asymptotic behavior,
classification of solutions.

Mathematics Subject Classification: Primary: 34K12, 34K40.

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