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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 $N_{i}^{'} (t) = N_{i} (t) [a_{i} (t) - \sum_{j = 1}^{n} β_{i j} (t) N_{j} (t) - \sum_{j = 1}^{n} b_{i j} (t) N_{j} (t - τ_{i j} (t)) - \sum_{j = 1}^{n} c_{i j} (t) N_{j}^{'} (t - τ_{i j} (t))] .$ As a corollary, we answer an open problem proposed by Y. Kuang.

Triangular numbers in geometric progression.

Chen, Yong-Gao; Fang, Jin-Hui — 2007

Integers

On $n ∣ ϕ (n) d (n) + 2$ and $n ∣ ϕ (n) σ (n) + 1$ .

Chen, Yong-Gao; Fang, Jin-Hui — 2008

Integers

On the subset sums of exponential type sequences

Yong-Gao Chen; Jin-Hui Fang; Norbert Hegyvári — 2016

Acta Arithmetica

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Periodic boundary value problems of impulsive differential equations.

Existence of periodic and subharmonic solutions for second-order $p$ -Laplacian difference equations.

Multiple periodic solutions for a discrete time model of plankton allelopathy.

Existence of weak solutions for second-order boundary value problem of impulsive dynamic equations on time scales.

Existence of positive periodic solutions for delayed predator-prey patch systems with stocking.

Nonexistence of a geometric progression that contains four triangular numbers.

Neither $\prod_{k = 1}^{n} (4 k 2 + 1)$ nor $\prod_{k = 1}^{n} (2 k (k - 1) + 1)$ is a perfect square.

Positive periodic solutions of $N$ -species neutral delay systems

Triangular numbers in geometric progression.

On $n ∣ ϕ (n) d (n) + 2$ and $n ∣ ϕ (n) σ (n) + 1$ .

On the subset sums of exponential type sequences