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Oscillation behavior of <f>n</f>th order neutral differential equations with continuous delay

Authors :
Candan, T.
Dahiya, R.S.
Source :
Journal of Mathematical Analysis & Applications. Feb2004, Vol. 290 Issue 1, p105. 8p.
Publication Year :
2004

Abstract

We consider the &lt;f&gt;n&lt;/f&gt;th order nonlinear neutral differential equation of the form &lt;fen&gt;&lt;cp type=&quot;lsqb&quot; STYLE=&quot;S&quot;&gt;x(t)+∫lower limit a, upper limit b p(t,μ)x&lt;fen&gt;&lt;cp type=&quot;lpar&quot; STYLE=&quot;S&quot;&gt;τ(t,μ)&lt;cp type=&quot;rpar&quot; STYLE=&quot;S&quot;&gt;&lt;/fen&gt; dμ&lt;cp type=&quot;rsqb&quot; STYLE=&quot;S&quot;&gt;&lt;/fen&gt;(n)+λ∫lower limit c, upper limit d q(t,ξ)f&lt;fen&gt;&lt;cp type=&quot;lpar&quot; STYLE=&quot;S&quot;&gt;x&lt;fen&gt;&lt;cp type=&quot;lpar&quot; STYLE=&quot;S&quot;&gt;σ(t,ξ)&lt;cp type=&quot;rpar&quot; STYLE=&quot;S&quot;&gt;&lt;/fen&gt;&lt;cp type=&quot;rpar&quot; STYLE=&quot;S&quot;&gt;&lt;/fen&gt; dξ=h(t). In this paper, we obtain sufficient conditions which ensure that all solutions are either oscillatory or &lt;f&gt;limt→∞&amp;z.sfnc;x(t)&amp;z.sfnc;=∞&lt;/f&gt; or else &lt;f&gt;liminft→∞&amp;z.sfnc;x(t)&amp;z.sfnc;=0.&lt;/f&gt; [Copyright &amp;y&amp; Elsevier]

Details

Language :
English
ISSN :
0022247X
Volume :
290
Issue :
1
Database :
Academic Search Index
Journal :
Journal of Mathematical Analysis & Applications
Publication Type :
Academic Journal
Accession number :
11960630
Full Text :
https://doi.org/10.1016/j.jmaa.2003.09.072