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Keywords:
positive periodic solutions; existence; neutral delay system
Summary:
In this paper, we employ some new techniques to study the existence of positive periodic solution of $n$-species neutral delay system \[ N^{\prime }_i(t)=N_i(t)\biggl [a_i(t)-\sum _{j=1}^n\beta _{ij}(t)N_j(t)- \sum _{j=1}^nb_{ij}(t)N_j(t-\tau _{ij}(t))-\sum _{j=1}^nc_{ij}(t) N^{\prime }_j(t-\tau _{ij}(t))\biggr ]. \] As a corollary, we answer an open problem proposed by Y. Kuang.
References:
[1] Y.  Kuang: Delay Differential Equations with Applications in Population Dynamics. Academic Press, New York, 1993. MR 1218880 | Zbl 0777.34002
[2] H. I. Freedman and J.  Wu: Periodic solutions of single-species models with periodic delay. SIAM J.  Math. Anal. 23 (1992), 689–701. MR 1158828
[3] L.  Erbe, W.  Krawcewicz and J.  Wu: A composite coincidence degree with applications to boundary value problems of neutral equations. Trans. Amer. Math. Soc. 335 (1993), 459–478. MR 1169080
[4] W. Krawcewicz and J.  Wu: Theory of Degrees with Applications to Bifurcations and Differential Equations. John Wiley & Sons, Inc., New York, 1996. MR 1426128
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