Unique positive solution for an alternative discrete Painlevé I equation
Unique positive solution for an alternative discrete Painlevé I equation
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替代离散 Painlevé I 方程的唯一正解
DOI：
10.1080/10236198.2015.1127917
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发表时间：
2015
影响因子：
1.1
通讯作者：
W. Van Assche
中科院分区：
文献类型：
--
作者：
P. Clarkson;A. Loureiro;W. Van Assche
我们证明了可选的离散painlevel方程（alt-）有一个对所有方程都保持正的唯一解。进一步，我们用涉及Airy函数的第二个painlev<s:1>方程（）的一个特殊解来确定这个正解。因此，只涉及Airy函数的特函数解具有对所有和所有都保持正的性质，这是对和所有-的特解的一个新的表征。
We show that the alternative discrete Painlevé I equation (alt-) has a unique solution which remains positive for all . Furthermore, we identify this positive solution in terms of a special solution of the second Painlevé equation () involving the Airy function . The special-function solutions of involving only the Airy function therefore have the property that they remain positive for all and all , which is a new characterization of these special solutions of and alt-.