On quadratically integrable solutions of the second order linear equation

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 \,. \

Conjugacy and disconjugacy criteria for second order linear ordinary differential equations

summary:Conjugacy and disconjugacy criteria are established for the equation $$u^{\prime \prime }+p(t)u=0\,,$$ where $p:]-\infty ,+\infty [\rightarrow ]-\infty ,+\infty [$ is a locally summable function