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second order linear equation; quadratically integrable solutions; vanishing at infinity solutions
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 \[ \int ^{+\infty }\frac{u^2(s)}{s^i}ds<+\infty \,. \]
[1] Wintner A.: On the non-existence of conjugate points. Amer. J. Math. 73 (1951), 368–380. MR 0042005
[2] Kneser A.: Untersuchung und asymptotische Darstellung der Integrale gewisser Differentialgleichungen bei grossen reelen Werten des Arguments. J. Reine Angew. Math. 116 (1896), 178–212.
[3] Kiguradze I.T., Chanturia T.A.: Asymptotic properties of solutions of nanautonomous ordinary differential equations. Kluwer Academic Publishers, Dordrecht–Boston–London, 1992.
[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
[5] Chantladze T., Kandelaki N., Lomtatidze A.: Oscillation and nonoscillation criteria for second order linear equations. Georgian Math. J. 6 (1999), No 5, 401–414. MR 1692963
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