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�������պ����ѧѧ�� 2000, Vol. 26 Issue (5) :608-611    DOI:
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Existence of Duck Solutions of A Kind of Differential Equations with Small Parameter
LI Cui-ping*
Beijing University of Aeronautics and Astronautics,School of Science

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Abstract�� A kind of one parameter planar singular perturbation equation is studied by the qualitative theory of ordinary differential equations,asymptotic analysis methods,implicit function theorem and fixed point methods.Some sufficient conditions are given to support the existence of duck solutions and duck cycles when the singular points of the system are in the small neighbourhood of turnning points.It is proved that there exists a value of parameter ��a=ac(ε)�� such that for ��a�� in a small neighbourhood of ��ac(ε)��,the systems have duck cycles.Moreover,the asymptotic estimation of corresponding duck solutions and duck cycles and the rule of changing of the duck cycles with parameter are obtained.The article 1 and 2 are the special cases of this paper.
Keywords�� asymptotic methods   qualitative theory   differential equations   singular perturbation   bifurcation   duck solution   duck cycle     
Received 1999-03-25;
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���Ƽ.һ�ຬС����΢�ַ���Ѽ��Ĵ�����[J]  �������պ����ѧѧ��, 2000,V26(5): 608-611
LI Cui-ping.Existence of Duck Solutions of A Kind of Differential Equations with Small Parameter[J]  JOURNAL OF BEIJING UNIVERSITY OF AERONAUTICS AND A, 2000,V26(5): 608-611
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