# On quadratically integrable solutions of the second order linear equation

T. Chantladze; Nodar Kandelaki; Alexander Lomtatidze

Archivum Mathematicum (2001)

- Volume: 037, Issue: 1, page 57-62
- ISSN: 0044-8753

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topChantladze, T., Kandelaki, Nodar, and Lomtatidze, Alexander. "On quadratically integrable solutions of the second order linear equation." Archivum Mathematicum 037.1 (2001): 57-62. <http://eudml.org/doc/248743>.

@article{Chantladze2001,

abstract = {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 \[ \int ^\{+\infty \}\frac\{u^2(s)\}\{s^i\}ds<+\infty \,. \]},

author = {Chantladze, T., Kandelaki, Nodar, Lomtatidze, Alexander},

journal = {Archivum Mathematicum},

keywords = {second order linear equation; quadratically integrable solutions; vanishing at infinity solutions; second order linear equation; quadratically integrable solutions; vanishing at infinity solutions},

language = {eng},

number = {1},

pages = {57-62},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {On quadratically integrable solutions of the second order linear equation},

url = {http://eudml.org/doc/248743},

volume = {037},

year = {2001},

}

TY - JOUR

AU - Chantladze, T.

AU - Kandelaki, Nodar

AU - Lomtatidze, Alexander

TI - On quadratically integrable solutions of the second order linear equation

JO - Archivum Mathematicum

PY - 2001

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 037

IS - 1

SP - 57

EP - 62

AB - 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 \[ \int ^{+\infty }\frac{u^2(s)}{s^i}ds<+\infty \,. \]

LA - eng

KW - second order linear equation; quadratically integrable solutions; vanishing at infinity solutions; second order linear equation; quadratically integrable solutions; vanishing at infinity solutions

UR - http://eudml.org/doc/248743

ER -

## References

top- Wintner A., On the non-existence of conjugate points, Amer. J. Math. 73 (1951), 368–380. (1951) MR0042005
- Kneser A., Untersuchung und asymptotische Darstellung der Integrale gewisser Differentialgleichungen bei grossen reelen Werten des Arguments, J. Reine Angew. Math. 116 (1896), 178–212.
- Kiguradze I.T., Chanturia T.A., Asymptotic properties of solutions of nanautonomous ordinary differential equations, Kluwer Academic Publishers, Dordrecht–Boston–London, 1992. (1992)
- 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. (1987) MR0925830
- Chantladze T., Kandelaki N., Lomtatidze A., Oscillation and nonoscillation criteria for second order linear equations, Georgian Math. J. 6 (1999), No 5, 401–414. (1999) MR1692963

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