Asymptotic decay of nonoscillatory solutions of general nonlinear difference equations

E. Thandapani, S. Lourdu Marian and John R. Graef

International Journal of Mathematics and Mathematical Sciences, 2001, vol. 27, 1-8

Abstract:

The authors consider the m th order nonlinear difference equations of the form D m y n + q n f ( y σ ( n ) ) = e i , where m ≥ 1 , n ∈ ℕ = { 0 , 1 , 2 , … } , a n i > 0 for i = 1 , 2 , … , m − 1 , a n m ≡ 1 , D 0 y n = y n , D i y n = a n i Δ D i − 1 y n , i = 1 , 2 , … , m , σ ( n ) → ∞ as n → ∞ , and f : ℝ → ℝ is continuous with u f ( u ) > 0 for u ≠ 0 . They give sufficient conditions to ensure that all bounded nonoscillatory solutions tend to zero as n → ∞ without assuming that ∑ n = 0 ∞ 1 / a n i = ∞ , i = 1 , 2 , … , m − 1 , { q n } is positive, or e n ≡ 0 as is often required. If { q n } is positive, they prove another such result for all nonoscillatory solutions.

Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:415039

DOI: 10.1155/S0161171201006172

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