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Keywords:
second order linear equation; quadratically integrable solutions; vanishing at infinity solutions
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 \[ \int ^{+\infty }\frac{u^2(s)}{s^i}ds<+\infty \,. \]
References:
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[4] Kiguradze I.T., Shekhter B.L.: Singular boundary value problems for second order differential equations. in “Current Problems in Mathematics: Newest Results,” vol. 30, pp. 105–201, Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyzn. Inst. Nauchn. i Tekhn. Inform., Moscow, 1987. MR 0925830
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