<?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%">CURTIS KUNKEL</style></author><author><style face="normal" font="default" size="100%">ASHLEY MARTIN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">POSITIVE SOLUTIONS TO SINGULAR HIGHER ORDER BOUNDARY VALUE PROBLEMS ON PURELY DISCRETE TIME SCALES</style></title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B16</style></keyword><keyword><style  face="normal" font="default" size="100%">34B18</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</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/19/4/7.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%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We study singular discrete higher order boundary value problems with mixed boundary conditions of the form $${ u^{∆^n} (t_{i−(n−1)}) + f(t_i , u(t_i), . . . , u^{∆^{n−1}} (t_{i−(n−1)})) = 0,}$$&amp;nbsp; $${ u^{∆^{n−1}} (t_0) = u^{∆^{n−2}} (t_{N+1}) = u^{∆^{n−3}} (t_{N+2}) = · · · = u^∆(t_{N+n−2}) = u(t_{N+n−1}) = 0, }$$ over a finite discrete interval ${ \mathbb{T} = {t_0, t_1, . . ., t_{N+n−2}, t_{N+n−1}}.}$ We prove the existence of a positive solution by means of the lower and upper solutions method and the Brouwer fixed point theorem in conjunction with perturbation methods to approximate regular problems.&lt;/p&gt;

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