BOUNDEDNESS OF SOLUTIONS OF SECOND-ORDER FORCED NONLINEAR DYNAMIC EQUATIONS

BOUNDEDNESS OF SOLUTIONS OF SECOND-ORDER FORCED NONLINEAR DYNAMIC EQUATIONS

In this paper, we give some sufficient conditions which ensure that every solution of a certain class of forced nonlinear dynamic equations of the form (*) xΔΔ(t) + qσ(t)f(x(t)) = r(t), on time scale T is bounded. To the best of our knowledge nothing is known regarding the qualitative behavior of so...

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Veröffentlicht in:The Rocky Mountain journal of mathematics 2006-01, Vol.36 (6), p.2027-2039
1. Verfasser: SAKER, S.H.
Format: Artikel
Sprache:eng
Schlagworte:
34A99
34C10
34K11
39A10
39A11
39A99
Boundedness
Calculus
Difference equations
Differential equations
Exponential functions
forced nonlinear dynamic equation
Mathematical theorems
Mathematics
positive solution
Sufficient conditions
time scale
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Zusammenfassung:In this paper, we give some sufficient conditions which ensure that every solution of a certain class of forced nonlinear dynamic equations of the form (*) xΔΔ(t) + qσ(t)f(x(t)) = r(t), on time scale T is bounded. To the best of our knowledge nothing is known regarding the qualitative behavior of solutions of the nonlinear dynamic equation (*) on time scales until now. Our results not only unify the boundedness of differential and difference equations but are also new for the q-difference equations.
ISSN:0035-7596
1945-3795
DOI:10.1216/rmjm/1181069359