# Article

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Keywords:
second order linear equation; quadratically integrable solutions; vanishing at infinity solutions
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 $\int ^{+\infty }\frac{u^2(s)}{s^i}ds<+\infty \,.$
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