<?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%">John R. Graef</style></author><author><style face="normal" font="default" size="100%">LINGJU KONG</style></author><author><style face="normal" font="default" size="100%">QINGKAI KONG</style></author><author><style face="normal" font="default" size="100%">MIN WANG</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A FRACTIONAL BOUNDARY VALUE PROBLEM WITH DIRICHLET BOUNDARY CONDITION</style></title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword><keyword><style  face="normal" font="default" size="100%">34B27</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.acadsol.eu/en/articles/19/4/2.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%">8</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, the authors study a nonlinear fractional boundary value problem consisting of the equation$${ −D^α_{0+}u + aD^β_{0+}u = w(t)f(u), \ \ \ 1 &amp;lt; α &amp;lt; 2, 0 ≤ β &amp;lt; 1, }$$ and the Dirichlet boundary condition. The associated Green’s function is derived in terms of the generalized Mittag-Leffler function, and the existence of solutions is established based on it.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue><section><style face="normal" font="default" size="100%">497</style></section></record><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%">QINGKAI KONG</style></author><author><style face="normal" font="default" size="100%">THOMAS E. ST. GEORGE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">MATCHING METHOD FOR NODAL SOLUTIONS OF BOUNDARY VALUE PROBLEMS WITH INTEGRAL BOUNDARY CONDITIONS</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/19/1/10.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%">19</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we study the nonlinear boundary value problem consisting of the equation ${ y′′+ \int^{b}_{a} &amp;nbsp;w(t, τ)f(y, τ) \ dζ(τ) = 0 }$ on&amp;nbsp; [a, b] and a double Riemann-Stieltjes integral boundary condition. We establish the existence of various nodal solutions of this problem by matching the solutions of two boundary value problems, each of which involves one separated boundary condition and open Riemann-Stieltjes integral boundary condition, at some point in (a, b). We also obtain the conditions for nonexistence of nodal solutions of this boundary value problem.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">129</style></section></record><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%">QINGKAI KONG</style></author><author><style face="normal" font="default" size="100%">MICHAEL MCCABE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">POSITIVE SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR HIGHER-ORDER NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS</style></title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword><keyword><style  face="normal" font="default" size="100%">34B18</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/19/4/5.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%">15</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;In this paper, we study the boundary value problem consisting of the higher-order fractional differential equation$${ (−1)^m (D^α_{0+})^m u = f(t, u), \ \ 0 &amp;lt; t &amp;lt; 1, }$$ and the boundary conditions $${ \left( (D^α_{0+})^i u \right)&amp;nbsp;(0) = \left( (D^α_{0+})^i u\right) (1) = 0, \ \ i = 0, 1, . . . , m − 1, }$$ where ${ 1 &amp;lt; α &amp;lt; 2, m ∈ \mathbb{N},\ \&amp;nbsp; D^α_{0+} }$ is the Riemann-Liouville fractional differential operator, and ${ \ {(}D^α_{0+})^{j+1} = D^α_{0+}\ {(} D^α_{0+}\ {)}^j}$&amp;nbsp;for ${ j = 0, . . . , m − 1, }$ with ${ \ {(}D^α_{0+}\ {)}^0 = I, }$ the identity operator. By finding the Green’s function using the iteration method and applying the Krasnosel’skii fixed point theorem, we establish the existence of one, two, any finite number, and even a countably infinite number of positive solutions. Criteria for the nonexistence of positive solutions are also obtained. Our results cover, improve, and complement those by Jiang and Yuan for the case&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue><section><style face="normal" font="default" size="100%">527</style></section></record><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%">John R. Graef</style></author><author><style face="normal" font="default" size="100%">LINGJU KONG</style></author><author><style face="normal" font="default" size="100%">QINGKAI KONG</style></author><author><style face="normal" font="default" size="100%">BO YANG</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">HIGHER ORDER BOUNDARY VALUE PROBLEMS WITH TWO POINT SEPARATED NONHOMOGENEOUS BOUNDARY CONDITIONS</style></title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword><keyword><style  face="normal" font="default" size="100%">34B18</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.acadsol.eu/en/articles/15/4/2.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">15</style></volume><pages><style face="normal" font="default" size="100%">22</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The authors study the 2n-th order nonlinear boundary value problems with two point separated nonhomogeneous boundary conditions u (2n) = g(t)f(t, u), t ∈ (0, 1),    αu(2i) (0) − βu(2i+1)(0) = (−1)iλ2i , γu(2i) (1) + δu(2i+1)(1) = (−1)iλ2i+1. i = 0, . . . , n − 1, Criteria are established for the existence of nontrivial solutions, positive solutions, and negative solutions of the above problem. Conditions are determined by the relationship between the behavior of the quotient f(t, x)/x for x near 0 and ∞, and the smallest positive characteristic values of some associated linear integral operator. This work improves and extends a number of recent results in the literature on this topic. The results are illustrated with examples.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue><section><style face="normal" font="default" size="100%">435</style></section></record><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%">QINGKAI KONG</style></author><author><style face="normal" font="default" size="100%">XIAOFEI WANG</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">NONLINEAR BOUNDARY VALUE PROBLEMS WITH p-LAPLACIAN</style></title><secondary-title><style face="normal" font="default" size="100%">Communications in Applied Analysis</style></secondary-title><short-title><style face="normal" font="default" size="100%">NONLINEAR BVPS WITH P-LAPLACIAN</style></short-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">99Z00</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">01/2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.acadsol.eu/en/articles/15/1/3.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">15</style></volume><pages><style face="normal" font="default" size="100%">46</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;div class=&quot;rtejustify&quot;&gt;We study the second order nonlinear boundary value problem with p-Laplacian consisting of the equation −[φ(y ′ )] ′ + q(t)φ(y) = w(t)f (y) with φ(y) = |y|&lt;sup&gt;p−1&lt;/sup&gt;y for p &amp;gt; 0 on [a, b] and a general separated boundary condition. By comparing it with a half-linear Sturm-Liouville problem we obtain conditions for the existence and nonexistence of nodal solutions of this problem. More specifically, let λ&lt;sub&gt;n&lt;/sub&gt; , n = 0, 1, 2, . . . , be the n-th eigenvalue of the corresponding half-linear Sturm-Liouville problem. Then the boundary value problem has a pair of solutions with exactly n zeros in (a, b) if λ n is in the interior of the range of f (y)/φ(y); and does not have any solution with exactly n zeros in (a, b) if λ&lt;sub&gt;n&lt;/sub&gt; is outside the range. These conditions become necessary and sufficient when f (y)/φ(y) is monotone on (−∞, 0) and on (0, ∞). We also study the changes of the number of different types of nodal solutions as the equation or the boundary condition changes. Our results are obtained based on the global existence and uniqueness of solutions of the corresponding initial value problems established earlier by the authors.&lt;/div&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><work-type><style face="normal" font="default" size="100%">scientific: mathematics</style></work-type><section><style face="normal" font="default" size="100%">25</style></section></record></records></xml>