| Title:
|
On asymptotic properties of solutions of third order linear differential equations with deviating arguments (English) |
| Author:
|
Kiguradze, Ivan |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
30 |
| Issue:
|
1 |
| Year:
|
1994 |
| Pages:
|
59-72 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The asymptotic properties of solutions of the equation $u^{\prime \prime \prime }(t)=p_1(t)u(\tau _1(t))+p_2(t)u^{\prime }(\tau _2(t))$, are investigated where $p_i:[a,+\infty [\rightarrow R \;\;\;\;(i=1,2)$ are locally summable functions, $\tau _i:[a,+\infty [\rightarrow R\;\;\;(i=1,2)$ measurable ones and $\tau _i(t)\ge t\;\;\;(i=1,2)$. In particular, it is proved that if $p_1(t)\le 0$, $p^2_2(t)\le \alpha (t)|p_1(t)|$, \[\int _a^{+\infty }[\tau _1(t)-t]^2p_1(t)dt<+\infty \;\;\;\text{and}\;\;\; \int _a^{+\infty }\alpha (t)dt<+\infty ,\] then each solution with the first derivative vanishing at infinity is of the Kneser type and a set of all such solutions forms a one-dimensional linear space. (English) |
| Keyword:
|
differential equation with deviating arguments |
| Keyword:
|
Kneser type solutions |
| Keyword:
|
vanishing at infiniting solution |
| MSC:
|
34K15 |
| MSC:
|
34K99 |
| idZBL:
|
Zbl 0806.34063 |
| idMR:
|
MR1282113 |
| . |
| Date available:
|
2008-06-06T21:25:39Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107495 |
| . |
| Reference:
|
[1] C. Villari: Contributi allo studio asintotico dell’ equazione $x^{\prime \prime \prime }(t)+p(t)x(t)=0 $.Ann. Math. Pura ed Appl., 51(1960), 301-328. Zbl 0095.06903, MR 0121528 |
| Reference:
|
[2] I. T. Kiguradze and D. I. Chichua: On the Kneser problem for functional differential equations.(Russian) Differentsial’nie Uravneniya 27 (1991), No 11, 1879-1892. MR 1199212 |
| Reference:
|
[3] I .T. Kiguradze: On some properties of solutions of second order linear functional differential equations.Proc. of the Georgian Acad. of Sciences, Mathematics 1 (1993), No 5, 545-553. Zbl 0810.34067, MR 1288650 |
| . |
