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Title: On the asymptotic behavior at infinity of solutions to quasi-linear differential equations (English)
Author: Astashova, Irina
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 135
Issue: 4
Year: 2010
Pages: 373-382
Summary lang: English
Category: math
Summary: Sufficient conditions are formulated for existence of non-oscillatory solutions to the equation $$y^{(n)}+\sum _{j=0}^{n-1}a_j(x)y^{(j)}+p(x)|y|^k \mathop {\rm sgn} y =0$$ with $ n\ge 1$, real (not necessarily natural) $k>1$, and continuous functions $p(x)$ and $a_j(x)$ defined in a neighborhood of $+\infty $. For this equation with positive potential $p(x)$ a criterion is formulated for existence of non-oscillatory solutions with non-zero limit at infinity. In the case of even order, a criterion is obtained for all solutions of this equation at infinity to be oscillatory. \endgraf Sufficient conditions are obtained for existence of solution to this equation which is equivalent to a polynomial. (English)
Keyword: quasi-linear ordinary differential equation of higher order
Keyword: existence of non-oscillatory solution
Keyword: oscillatory solution
MSC: 34C10
MSC: 34C15
idZBL: Zbl 1224.34098
idMR: MR2681011
DOI: 10.21136/MB.2010.140828
Date available: 2010-11-24T08:25:33Z
Last updated: 2020-07-29
Stable URL:
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