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<mrnumber>MR3099036</mrnumber>
<author>Tongxing LI, Yuri V. ROGOVCHENKO and Chenghui ZHANG</author>
<author_utf8>Tongxing LI, Yuri V. ROGOVCHENKO and Chenghui ZHANG</author_utf8>
<title>Oscillation of Second-Order Neutral Differential Equations</title>
<journal>Funkcialaj Ekvacioj. Serio Internacia</journal>
<volume>56</volume>
<year>2013</year>
<page>111--120</page>
<url_pdf>http://fe.math.kobe-u.ac.jp/FE/FullPapers/56-1/56_111.pdf</url_pdf>
<mathsci_link>http://www.ams.org/mathscinet-getitem?mr=MR3099036</mathsci_link>
<abstract>We study oscillatory behavior of a class of second-order neutral differential equations relating oscillation of these equations to existence of positive solutions to associated first-order functional differential inequalities. Our assumptions allow applications to differential equations with both delayed and advanced arguments, and not only. New theorems complement and improve a number of results reported in the literature. Two illustrative examples are provided.</abstract>
<keywords>Oscillation, Neutral differential equations, Delayed arguments, Advanced arguments, Positive solutions, Comparison.</keywords>
<subject>34K11.</subject>
<fesi_info>
  <FILE>56-111</FILE>
  <YEAR>2013</YEAR>
  <TITLE>Oscillation of Second-Order Neutral Differential Equations</TITLE>
  <AUTHOR>Tongxing LI, Yuri V. ROGOVCHENKO and Chenghui ZHANG</AUTHOR>
  <AUTHOR_utf8>Tongxing LI, Yuri V. ROGOVCHENKO and Chenghui ZHANG</AUTHOR_utf8>
</fesi_info>

<references>


<article>
<bibitem>1</bibitem>
<author>Agarwal, Ravi P.; Grace, Said R.</author>
<title>Oscillation theorems for certain neutral functional differential equations</title>
<journal>Comput. Math. Appl.</journal>
<vol>38</vol>
<year>1999</year>
<page>1-11</page>
<mr>MR1729800</mr>
</article>


<book>
<bibitem>2</bibitem>
<author>Agarwal, Ravi P.; Grace, Said R.; O'Regan, Donal</author>
<booktitle>Oscillation Theory for Difference and Functional Differential Equations</booktitle>
<publisher>Kluwer Academic Publishers, Dordrecht</publisher>
<year>2000</year>
<mr>MR1774732</mr>
</book>


<article>
<bibitem>3</bibitem>
<author>Agarwal, Ravi P.; Grace, Said R.; O'Regan, Donal</author>
<title>Oscillation criteria for certain $n$-th order differential equations with deviating arguments</title>
<journal>J. Math. Anal. Appl.</journal>
<vol>262</vol>
<year>2001</year>
<page>601-622</page>
<mr>MR1859327</mr>
</article>


<article>
<bibitem>4</bibitem>
<author>Bacul&#237;kov&#225;, Blanka; D&#382;urina, Jozef</author>
<title>Oscillation theorems for second order neutral differential equations</title>
<journal>Comput. Math. Appl.</journal>
<vol>61</vol>
<year>2011</year>
<page>94-99</page>
<mr>MR2739438</mr>
</article>


<article>
<bibitem>5</bibitem>
<author>Bacul&#237;kov&#225;, Blanka; D&#382;urina, Jozef</author>
<title>Oscillation theorems for second order nonlinear neutral differential equations</title>
<journal>Comput. Math. Appl.</journal>
<vol>62</vol>
<year>2011</year>
<page>4472-4478</page>
<mr>MR2855589</mr>
</article>


<article>
<bibitem>6</bibitem>
<author>Bacul&#237;kov&#225;, Blanka; D&#382;urina, Jozef; Li, Tongxing</author>
<title>Oscillation results for even-order quasilinear neutral functional differential equations</title>
<journal>Electron. J. Differential Equations</journal>
<vol>2011</vol>
<year>2011</year>
<page>No. 143, 9pp</page>
<mr>MR2853029</mr>
</article>


<book>
<bibitem>7</bibitem>
<author>Erbe, Lynn; Kong, Qingkai; Zhang, Binggen</author>
<booktitle>Oscillation Theory for Functional Differential Equations</booktitle>
<publisher>Monographs and Textbooks in Pure and Applied Mathematics, 190, Marcel Dekker, Inc., New York</publisher>
<year>1995</year>
<mr>MR1309905</mr>
</book>


<article>
<bibitem>8</bibitem>
<author>Grace, Said R.; Lalli, B. S.</author>
<title>Oscillation of nonlinear second order neutral delay differential equations</title>
<journal>Rad. Mat.</journal>
<vol>3</vol>
<year>1987</year>
<page>77-84</page>
<mr>MR0910068</mr>
</article>


<article>
<bibitem>9</bibitem>
<author>Grammatikopoulos, M. K.; Ladas, G.; Meimaridou, A.</author>
<title>Oscillation of second order neutral delay differential equation</title>
<journal>Rad. Mat.</journal>
<vol>1</vol>
<year>1985</year>
<page>267-274</page>
<mr>MR0827474</mr>
</article>


<article>
<bibitem>10</bibitem>
<author>Han, Zhenlai; Li, Tongxing; Sun, Shurong; Sun, Yibing</author>
<title>Remarks on the paper [Appl. Math. Comput. 207 (2009) 388-396]</title>
<journal>Appl. Math. Comput.</journal>
<vol>215</vol>
<year>2010</year>
<page>3998-4007</page>
<mr>MR2578865</mr>
</article>


<article>
<bibitem>11</bibitem>
<author>Hasanbulli, Mustafa; Rogovchenko, Yuri V.</author>
<title>Oscillation criteria for second order nonlinear neutral differential
equations</title>
<journal>Appl. Math. Comput.</journal>
<vol>215</vol>
<year>2010</year>
<page>4392-4399</page>
<mr>MR2596116</mr>
</article>


<book>
<bibitem>12</bibitem>
<author>Ladde, G. S.; Lakshmikantham, V.; Zhang, B. G.</author>
<booktitle>Oscillation Theory  of Differential Equations with Deviating Arguments</booktitle>
<publisher>Monographs and Textbooks in Pure and Applied Mathematics, 110, Marcel Dekker, Inc., New York</publisher>
<year>1987</year>
<mr>MR1017244</mr>
</book>


<article>
<bibitem>13</bibitem>
<author>Li, Tongxing</author>
<title>Comparison theorems for second-order neutral differential equations of mixed type</title>
<journal>Electron. J. Differential Equations</journal>
<vol>2010</vol>
<year>2010</year>
<page>No. 167, 7pp</page>
<mr>MR2740608</mr>
</article>


<article>
<bibitem>14</bibitem>
<author>Li, Tongxing; Agarwal, Ravi P.; Bohner, Martin</author>
<title>Some oscillation results for second-order neutral differential equations</title>
<journal>J. Indian Math. Soc. (N.S.)</journal>
<vol>79</vol>
<year>2012</year>
<page>97-106</page>
<mr>MR2976028</mr>
</article>


<article>
<bibitem>15</bibitem>
<author>Li, Tongxing; Han, Zhenlai; Zhang, Chenghui; Li, Hua</author>
<title>Oscillation criteria for second-order superlinear neutral differential equations</title>
<journal>Abstr. Appl. Anal.</journal>
<vol>2011</vol>
<year>2011</year>
<page>Art. ID 367541, 17pp</page>
<mr>MR2776752</mr>
</article>


</references>
</top_article>
