ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF OSCILLATOR EQUATIONS WITH SUBLINEAR DAMPING

Janos Karsai; John R. Graef; CHUANXI QIAN

Title	ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF OSCILLATOR EQUATIONS WITH SUBLINEAR DAMPING
Publication Type	Journal Article
Year of Publication	2002
Authors	Karsai, J, Graef, JR, QIAN, CHUANXI
Volume	6
Issue	1
Start Page	49
Pagination	11
Date Published	2002
ISSN	1083-2564
AMS	34C15, 34D05, 34D20
Abstract	We consider the nonlinear equation $${ x′′ + g(x ′ ) + f(x) = 0 \ \ \ (t ≥ 0),}$$ where the functions ${f}$ and ${g}$ satisfy the sign condition and ${g}$ is sublinear. It is known that if ${ f(x) = x}$ and ${ g(y) = by \ (\|b\| ≤ 2) }$ or ${f(x) = x }$ and ${g(y) = \|y\|^β sign \ y, \ β > 1,}$ then the solutions are oscillatory. As a consequence of a more general result, we prove that if ${ f(x) = x }$ and ${g(y) = \|y\|^β \ sign \ y, \ 0 < β < 1,}$ i.e., ${g}$ is sublinear, then the solutions are eventually monotonic, and we give estimates for their asymptotic behavior.
URL	http://www.acadsol.eu/en/articles/6/1/4.pdf
Refereed Designation	Refereed
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