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Reverse‐Order Lower and Upper Functions for Periodic Problems of Second‐Order Singular Difference Equations

Author

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  • Yanqiong Lu
  • Ruyun Ma

Abstract

We present sufficient conditions ensuring the lower and upper functions on the reversed‐order for the periodic difference equations. This enables us to obtain the existence of positive periodic solutions of the second‐order difference equation Δ2u(t − 1) = g(t)/uμ (t) − h(t)/uλ (t) + f(t), t ∈ ℤ, where g, h : ℤ → [0, ∞), and f : ℤ → ℝ are T‐periodic functions, λ, μ > 0.

Suggested Citation

  • Yanqiong Lu & Ruyun Ma, 2013. "Reverse‐Order Lower and Upper Functions for Periodic Problems of Second‐Order Singular Difference Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:176465
    DOI: 10.1155/2013/176465
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    References listed on IDEAS

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    1. Ruyun Ma & Yanqiong Lu & Tianlan Chen, 2012. "Existence of One‐Signed Solutions of Discrete Second‐Order Periodic Boundary Value Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. Ruyun Ma & Yanqiong Lu & Tianlan Chen, 2012. "Existence of One-Signed Solutions of Discrete Second-Order Periodic Boundary Value Problems," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-13, December.
    3. Haishen Lü & Donal O'regan & Ravi P. Agarwal, 2006. "A positive solution for singular discrete boundary value problems with sign-changing nonlinearities," International Journal of Stochastic Analysis, Hindawi, vol. 2006, pages 1-14, January.
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