Value distribution of meromorphic solutions of certain difference Painlevé equations |
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| Authors: | Zong-Xuan Chen |
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| Institution: | a School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, PR China
b Department of Mathematics, College of Natural Sciences, Pusan National University, Pusan 609-735, Republic of Korea |
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| Abstract: | The Borel exceptional value and the exponents of convergence of poles, zeros and fixed points of finite order transcendental meromorphic solutions for difference Painlevé I and II equations are estimated. And the forms of rational solutions of the difference Painlevé II equation and the autonomous difference Painlevé I equation are also given. It is also proved that the non-autonomous difference Painlevé I equation has no rational solution. |
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| Keywords: | Difference Painlevé equation Borel exceptional value Rational solution |
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