ON THE OSCILLATORY AND ASYMPTOTIC BEHAVIOUR OF THIRD ORDER RETARDED DIFFERENTIAL EQUATIONS

TitleON THE OSCILLATORY AND ASYMPTOTIC BEHAVIOUR OF THIRD ORDER RETARDED DIFFERENTIAL EQUATIONS
Publication TypeJournal Article
Year of Publication2005
AuthorsSimeonov, PS
Volume9
Issue3
Start Page397
Pagination12
Date Published2005
ISSN1083-2564
AMS34K15
Abstract

The third order retarded differential equations$${ (r_2(t)(r_1(t)x ′ (t))′ ) ′ + p(t)x(g(t)) = 0 \ \ \ \ \ \ \ \ \ (L) }$$ and $${ (r_2(t)(r_1(t)x ′ (t))′ ) ′ + p(t)F(x(g(t))) = 0 \ \ \ \ \ \ \ \ (N) }$$are considered and sufficient conditions are obtained under which every proper solution ${x}$ of equation ${ (L) \ (or \ (N)) }$ is either oscillatory or such that $${ \lim_{t→+∞} x(t) = \lim_{t→+∞} r_1(t)x ′ (t) = \lim_{t→+∞} r_2(t)(r_1(t)x ′ (t))′ = 0 }$$ monotonically.
URLhttp://www.acadsol.eu/en/articles/9/3/10.pdf
Refereed DesignationRefereed
Full Text

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