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Positive periodic solutions of discrete Lotka-Volterra competition systems with state dependent and distributed delays. (English) Zbl 1125.39006

The author uses a fixed point theorem for strict set-contractions in cones, in order to establish existence of positive periodic solutions for a discrete competitive Lotka-Volterra system with state-dependent and distributed delays, namely
\[ \Delta x_i(n) = x_i(n) \left[ F_i(x)(n) - \sum_{j=1}^pb_{ij}(n)\sum_{\theta=-T_{ij}}^0H_{ij}(\theta)x_j(n+\theta) \right] \]
for \(1\leq i\leq p\) with functionals
\[ F_i(x)(n):=a_i(n)-\sum_{j=1}^p a_{ij}(n)x_j(f_{ij}(n,x_1(n),\dots,x_p(n))). \]

MSC:

39A14 Partial difference equations
39A12 Discrete version of topics in analysis
92D25 Population dynamics (general)
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References:

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