WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 15, 2016
Positive Periodic Solutions in Shifts δ± for a Neutral Delay Logistic Equation on Time Scales
Authors: ,
Abstract: Let $$\mathbb{T} \subset \mathbb{R} $$ be a periodic time scale in shifts $$ δ±$$ with period $$P ∈ (t0, ∞)_{\mathbb{T}} $$ and $$t_{0} \in \mathbb{T} $$ is nonnegative and fixed. By using a fixed point theorem of strict-set-contraction, some criteria are established for the existence of positive periodic solutions in shifts $$ δ±$$ for a neutral delay logistic equation on time scales of the form $$x^{Δ}(t)=x(t) \left [r(t) − a(t)x(t)- \sum_{j=1}^{n} b_{j} (t)x(δ−(τ_{j} , t)) − \sum_{j=1}^{n} c_{j} (t) x^{Δ} (δ−(ξ_{j} , t))
\right ] , t \mathbb{T}$$. Finally, two numerical examples are presented to illustrate the feasibility and effectiveness of the results.
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Keywords: Positive periodic solution, Neutral delay logistic equation, Strict-set-contraction, Shift operator, Time scale
Pages: 156-165
WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 15, 2016, Art. #15