Periodic solution of neutral Lotka-Volteffa system with periodic delays

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:324

Article

Liu, Zhijun ; Chen, Lansun

关键词: positive periodic solution;    neutral delay;    existence theorem;    Lotka-Volterra system;   

DOI  :  10.1016/j.jmaa.2005.12.029

来源: Elsevier

【 摘 要 】

A nonautonomous n-species Lotka-Volterra system with neutral delays is investigated. A set of verifiable sufficient conditions is derived for the existence of at least one strictly positive periodic solution of this Lotka-Volterra system by applying an existence theorem and some analysis techniques, where the assumptions of the existence theorem are different from that of Gaines and Mawhin's continuation theorem [R.E. Gaines, J.L. Mawhin, Coincidence Degree and Nonlinear Differential Equations, Springer-Verlag, Berlin, 1977] and that of abstract continuation theory for k-set contraction [W. Petryshyn, Z. Yu, Existence theorem for periodic solutions of higher order nonlinear periodic boundary value problems, Nonlinear Anal. 6 (1982) 943-969]. Moreover, a problem proposed by Freedman and Wu [H.I. Freedman, J. Wu, Periodic solution of single species models with periodic delay, SIAM J. Math. Anal. 23 (1992) 689-701] is answered. (c) 2005 Elsevier Inc. All rights reserved.

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