Geodesic
On quadratically integrable solutions of the second order linear equation
Archivum mathematicum, Tome 37 (2001) no. 1, pp. 57-62 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 \[ \int ^{+\infty }\frac{u^2(s)}{s^i}ds+\infty \,. \]
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 \[ \int ^{+\infty }\frac{u^2(s)}{s^i}ds+\infty \,. \]
Classification : 34C11
Keywords: second order linear equation; quadratically integrable solutions; vanishing at infinity solutions 
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Chantladze, T.; Kandelaki, N.; Lomtatidze, A. On quadratically integrable solutions of the second order linear equation. Archivum mathematicum, Tome 37 (2001) no. 1, pp. 57-62. http://geodesic.mathdoc.fr/item/ARM_2001_37_1_a6/

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