Positive periodic solutions of N -species neutral delay systems

Hui Fang

Czechoslovak Mathematical Journal (2003)

  • Volume: 53, Issue: 3, page 561-570
  • ISSN: 0011-4642

Abstract

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In this paper, we employ some new techniques to study the existence of positive periodic solution of n -species neutral delay system N i ' ( t ) = N i ( t ) a i ( t ) - ∑ j = 1 n β i j ( t ) N j ( t ) - ∑ j = 1 n b i j ( t ) N j ( t - τ i j ( t ) ) - ∑ j = 1 n c i j ( t ) N j ' ( t - τ i j ( t ) ) . As a corollary, we answer an open problem proposed by Y. Kuang.

How to cite

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Fang, Hui. "Positive periodic solutions of $N$-species neutral delay systems." Czechoslovak Mathematical Journal 53.3 (2003): 561-570. <http://eudml.org/doc/30799>.

@article{Fang2003,
abstract = {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.},
author = {Fang, Hui},
journal = {Czechoslovak Mathematical Journal},
keywords = {positive periodic solutions; existence; neutral delay system; positive periodic solutions; existence; neutral delay system},
language = {eng},
number = {3},
pages = {561-570},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Positive periodic solutions of $N$-species neutral delay systems},
url = {http://eudml.org/doc/30799},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Fang, Hui
TI - Positive periodic solutions of $N$-species neutral delay systems
JO - Czechoslovak Mathematical Journal
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 3
SP - 561
EP - 570
AB - 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.
LA - eng
KW - positive periodic solutions; existence; neutral delay system; positive periodic solutions; existence; neutral delay system
UR - http://eudml.org/doc/30799
ER -

References

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  1. Delay Differential Equations with Applications in Population Dynamics, Academic Press, New York, 1993. (1993) Zbl0777.34002MR1218880
  2. 10.1137/0523035, SIAM J.  Math. Anal. 23 (1992), 689–701. (1992) MR1158828DOI10.1137/0523035
  3. 10.1090/S0002-9947-1993-1169080-3, Trans. Amer. Math. Soc. 335 (1993), 459–478. (1993) MR1169080DOI10.1090/S0002-9947-1993-1169080-3
  4. Theory of Degrees with Applications to Bifurcations and Differential Equations, John Wiley & Sons, Inc., New York, 1996. (1996) MR1426128

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