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 \[ \int ^{+\infty }\frac{u^2(s)}{s^i}ds<+\infty \,. \]
@article{107786,
author = {T. Chantladze and Nodar Kandelaki and Alexander Lomtatidze},
title = {On quadratically integrable solutions of the second order linear equation},
journal = {Archivum Mathematicum},
volume = {037},
year = {2001},
pages = {57-62},
zbl = {1090.34537},
mrnumber = {1822762},
language = {en},
url = {http://dml.mathdoc.fr/item/107786}
}
Chantladze, T.; Kandelaki, Nodar; Lomtatidze, Alexander. On quadratically integrable solutions of the second order linear equation. Archivum Mathematicum, Tome 037 (2001) pp. 57-62. http://gdmltest.u-ga.fr/item/107786/
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