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a number 36-gauge. At times, when abrasion resistance is less of a concern, explorers will install a high-tensile, thinner, 18-gauge, twisted line. However, beware of thinner lines, as they may not offer sufficient strength, and of thicker lines, which require needlessly large re[r]

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φ= 0.(3.11)Then (1.1) has a positive periodic solution.4. Applications to population dynamicsIn this section, we apply our results from the previous section and show that some popu-lation models admit the existence of a positive periodic solution. We start by consideringY. N. Raffou[r]

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[13] W T. Li, Classification schemes for nonoscillatory solutions of two-dimensional nonlinear differ-ence systems,Comput.Math.Appl.42 (2001), no. 3–5, 341–355.[14] W. T. Patula, Growth and oscillation properties of second order linear difference equations,SIAMJ. Math. Anal. 10 (1979), no. 1, 55–61.[15[r]

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) contains only theidentity function;(ii) for δ>1, Ᏺ1δ(I,M,M∗) is empty and for δ = 1, Ᏺ1δ(I,M,M∗) contains only the iden-tity function.Proof. (i) Let φ ∈ ᏾1(I,M,M∗), where 0 ≤ M<1. Clearly φ is a strict contraction withLipschitz constant M on I.Soφ has a unique fixed poin[r]

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