| 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:
|
http://hdl.handle.net/10338.dmlcz/140828 |
| . |
| Reference:
|
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