A. Lomtatidze, Department of Mathematical Analysis, Masaryk University, Janackovo nam. 2a, 662 95 Brno, CZECH REPUBLIC
E-mail: bacho@math.muni.cz
Abstract. Integral criteria are established for $\dim V_i(p)=0$
and $\dim V_i(p)=1, i\in \{0,1\}$, where $V_i(p)$ is the space of solutions
$u$ of the equation
$$ u''+p(t)u=0 $$ satisfying the condition $$ \int^{+\infty}\frac{u^2(s)}{s^i}ds<+\infty\,.
$$
AMSclassification. 34C11
Keywords. Second order linear equation, quadratically integrable solutions, vanishing at infinity solutions