Positive periodic solutions of second-order difference equations with weak singularities

• Published in: Advances in difference equations Vol. 2012; no. 1; pp. 1 - 11
• Main Authors: Ma, Ruyun, Lu, Yanqiong
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 27.06.2012; Springer Nature B.V; BioMed Central Ltd
• Subjects: Analysis; Classifications; Difference and Functional Equations; Difference equations; Existence theorems; Functional Analysis; Functions (mathematics); Mathematical analysis; Mathematics; Mathematics and Statistics; Ordinary Differential Equations; Partial Differential Equations; Singularities; Theorems; Schauder's fixed point theorem; positive periodic solutions; weak singularities; difference equations
• ISSN: 1687-1847; 1687-1839; 1687-1847
• DOI: 10.1186/1687-1847-2012-90

We study the existence of positive periodic solutions of the second-order difference equation Δ 2 u ( t - 1 ) + a ( t ) u ( t ) = f ( t , u ( t ) ) + c ( t ) , t ∈ ℤ via Schauder's fixed point theorem, where a, c : ℤ → ℝ + are T -periodic functions, f ∈ C (ℤ × (0, ∞ ), ℝ) is T -periodic with respect to t and singular at u = 0. Mathematics Subject Classifications: 34B15.