Oscillation of perturbed nonlinear dynamic equations on time scales

In this paper we consider the oscillatory and asymptotic behavior of bounded solutions of second‐order nonlinear perturbed dynamic equation (α(t)(xΔ(t))r)Δ+ F(t,xσ (t)) = G(t, xσ (t), xΔ (t)), t ∈T , (0.1) where r = k/l with k even and l odd positive integer. Some new sufficient conditions are obtai...

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Published in:Zeitschrift für angewandte Mathematik und Mechanik 2005-10, Vol.85 (10), p.755-760
Main Authors: Sun, H.-R., Li, W.-R.
Format: Article
Language:English
Subjects:
dynamic equation
Exact sciences and technology
Finite differences and functional equations
Mathematical analysis
Mathematics
Ordinary differential equations
oscillation
Sciences and techniques of general use
time scales
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description In this paper we consider the oscillatory and asymptotic behavior of bounded solutions of second‐order nonlinear perturbed dynamic equation (α(t)(xΔ(t))r)Δ+ F(t,xσ (t)) = G(t, xσ (t), xΔ (t)), t ∈T , (0.1) where r = k/l with k even and l odd positive integer. Some new sufficient conditions are obtained for all bounded solutions of (0.1) to be oscillatory. Several examples that dwell upon the importance of our results are also included. In particular, our criteria extend some earlier results.
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subjects dynamic equation
Exact sciences and technology
Finite differences and functional equations
Mathematical analysis
Mathematics
Ordinary differential equations
oscillation
Sciences and techniques of general use
time scales
title Oscillation of perturbed nonlinear dynamic equations on time scales
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