| Title:
|
On quadratically integrable solutions of the second order linear equation (English) |
| Author:
|
Chantladze, T. |
| Author:
|
Kandelaki, N. |
| Author:
|
Lomtatidze, A. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
37 |
| Issue:
|
1 |
| Year:
|
2001 |
| Pages:
|
57-62 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Integral criteria are established for $\dim V_i(p)=0$ and $\dim V_i(p)=1, i\in \lbrace 0,1\rbrace $, where $V_i(p)$ is the space of solutions $u$ of the equation \[ u^{\prime \prime }+p(t)u=0 \] satisfying the condition \[ \int ^{+\infty }\frac{u^2(s)}{s^i}ds<+\infty \,. \] (English) |
| Keyword:
|
second order linear equation |
| Keyword:
|
quadratically integrable solutions |
| Keyword:
|
vanishing at infinity solutions |
| MSC:
|
34C11 |
| idZBL:
|
Zbl 1090.34537 |
| idMR:
|
MR1822762 |
| . |
| Date available:
|
2008-06-06T22:28:18Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107786 |
| . |
| Reference:
|
[1] Wintner A.: On the non-existence of conjugate points.Amer. J. Math. 73 (1951), 368–380. MR 0042005 |
| Reference:
|
[2] Kneser A.: Untersuchung und asymptotische Darstellung der Integrale gewisser Differentialgleichungen bei grossen reelen Werten des Arguments.J. Reine Angew. Math. 116 (1896), 178–212. |
| Reference:
|
[3] Kiguradze I.T., Chanturia T.A.: Asymptotic properties of solutions of nanautonomous ordinary differential equations.Kluwer Academic Publishers, Dordrecht–Boston–London, 1992. |
| Reference:
|
[4] Kiguradze I.T., Shekhter B.L.: Singular boundary value problems for second order differential equations.in “Current Problems in Mathematics: Newest Results,” vol. 30, pp. 105–201, Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyzn. Inst. Nauchn. i Tekhn. Inform., Moscow, 1987. MR 0925830 |
| Reference:
|
[5] Chantladze T., Kandelaki N., Lomtatidze A.: Oscillation and nonoscillation criteria for second order linear equations.Georgian Math. J. 6 (1999), No 5, 401–414. MR 1692963 |
| . |
