<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">XUEYAN LIU</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">THE SOLUTION MATCHING BY LIAPUNOV THEORY OF BVPS WITH ODD GAPS IN BOUNDARY CONDITIONS FOR nTH ORDER DIFFERENTIAL EQUATIONS</style></title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B10</style></keyword><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.acadsol.eu/en/articles/19/4/9.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;We are concerned with the existence and uniqueness of solutions to boundary value problems on an interval [a, c] for the nth order ordinary differential equation ${ y^{(n)} = f(x, y, y′ , . . . , y^{(n−1)}), }$ for ${n ≥ 3,}$ by matching solutions on [a, b] with solutions on [b, c] to extend the interval of existence for solutions. In this paper, we consider a general case where the gap in boundary conditions at b is odd. Different from the literature, we use Liapunov theory to deal with the case&lt;/p&gt;
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