In this paper, some misunderstam igs concerning the necessary conditions for resonance for ordinary differential equations with turning point have been corrected, and a recursive process for finding the sequence of ne...In this paper, some misunderstam igs concerning the necessary conditions for resonance for ordinary differential equations with turning point have been corrected, and a recursive process for finding the sequence of necessary conditions for resonance has beenoffered.展开更多
We study the Painlevé property of the （1＋1）-dimensional equations arising from the symmetry reduction for the （2＋1）- dimensional ones. Firstly, we derive the similarity reduction of the （2＋1）-dimensional...We study the Painlevé property of the （1＋1）-dimensional equations arising from the symmetry reduction for the （2＋1）- dimensional ones. Firstly, we derive the similarity reduction of the （2＋1）-dimensional potential Calogero-Bogoyavlenskii- Schiff （CBS） equation and Konopelchenko-Dubrovsky （KD） equations with the optimal system of the admitted one-dimensional subalgebras. Secondly, by analyzing the reduced CBS, KD, and Burgers equations with Painlevé test, re-spectively, we find both the Painlevé integrability, and the number and location of resonance points are invariant, if the similarity variables include all of the independent variables.展开更多
An existence-uniqueness result is given for second order nonlinear differential equations with Robin boundary conditionwhere αi, βi,(i =1,2), α and b are all constants.And the resonant points of this problemare als...An existence-uniqueness result is given for second order nonlinear differential equations with Robin boundary conditionwhere αi, βi,(i =1,2), α and b are all constants.And the resonant points of this problemare also evaluated.AMS(MOS) Subject classifications 34B15展开更多
基金Projects Supported by the Science Fund of the Chinese Academy of Sciences
文摘In this paper, some misunderstam igs concerning the necessary conditions for resonance for ordinary differential equations with turning point have been corrected, and a recursive process for finding the sequence of necessary conditions for resonance has beenoffered.
基金Project supported by the Natural Science Foundation of Shandong Province,China(Grant Nos.ZR2011AQ017 and ZR2010AM028)the Fundamental Research Funds for the Central Universities of Ministry of Education of China(Grant No.13CX02010A)
文摘We study the Painlevé property of the （1＋1）-dimensional equations arising from the symmetry reduction for the （2＋1）- dimensional ones. Firstly, we derive the similarity reduction of the （2＋1）-dimensional potential Calogero-Bogoyavlenskii- Schiff （CBS） equation and Konopelchenko-Dubrovsky （KD） equations with the optimal system of the admitted one-dimensional subalgebras. Secondly, by analyzing the reduced CBS, KD, and Burgers equations with Painlevé test, re-spectively, we find both the Painlevé integrability, and the number and location of resonance points are invariant, if the similarity variables include all of the independent variables.
文摘An existence-uniqueness result is given for second order nonlinear differential equations with Robin boundary conditionwhere αi, βi,(i =1,2), α and b are all constants.And the resonant points of this problemare also evaluated.AMS(MOS) Subject classifications 34B15
