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

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

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...

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Veröffentlicht in:Abstract and Applied Analysis 2013-01, Vol.2013 (2013), p.222-226-122
Hauptverfasser: Lu, Yanqiong, Ma, Ruyun
Format: Artikel
Sprache:eng
Schlagworte:
Difference equations
Existence theorems
Mathematical research
Periodic functions
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Beschreibung
Zusammenfassung: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.
ISSN:1085-3375
1687-0409
DOI:10.1155/2013/176465