Staff Members - Benha University
Oscillation and nonoscillation of nonlinear second order difference equations
• 2006
Publication Information
Authors
M. M. A. El-Sheikh, M. H. Abd Alla and E. M. El-Maghrabi (E. Awwad)
Keywords
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publication.type
International
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Supplementary Materials
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Abstract
In this paper, we study oscillation and nonoscillation behaviour of the second order
nonlinear difference equations of the form Δ (r_n ψ (x_n) Δ x_n)+ q_ n+ 1 f (x_ n+ 1)= 0, n ∈
N (n_o), and Δ (r_n ψ (x_n) Δ x_n)+ q_n f (n, x_n)= 0, n ∈ N (n_o), where N (no)= no, no+
1,…,(no is a fixed nonnegative integer number), Δx n= xn+ 1− xn is the forward difference
operator, x: N (no)→ ℝ, r: N (no)→(0,∞), Ψ: ℝ→(0,∞), f is a real valued continuous function,
and qn is a sequence of real valued.
nonlinear difference equations of the form Δ (r_n ψ (x_n) Δ x_n)+ q_ n+ 1 f (x_ n+ 1)= 0, n ∈
N (n_o), and Δ (r_n ψ (x_n) Δ x_n)+ q_n f (n, x_n)= 0, n ∈ N (n_o), where N (no)= no, no+
1,…,(no is a fixed nonnegative integer number), Δx n= xn+ 1− xn is the forward difference
operator, x: N (no)→ ℝ, r: N (no)→(0,∞), Ψ: ℝ→(0,∞), f is a real valued continuous function,
and qn is a sequence of real valued.