Geodesic
Conditions for non-oscillation of singular linear differential equations of second order
Matematičeskie zametki, Tome 6 (1969) no. 5, pp. 633-639.

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Conditions are found in the fulfillment of which each non-trivial solution of the equation uPrime+ $u''+\beta(t)u'+\alpha(t)u=0$, where $\beta(t)\in L(a,b)$ and $(t-a)(t-b)\alpha(t)\in L(a,b)$ has not more than one zero on the interval $a\le t\le b$. 
@article{MZM_1969_6_5_a14,
     author = {I. T. Kiguradze},
     title = {Conditions for non-oscillation of singular linear differential equations of second order},
     journal = {Matemati\v{c}eskie zametki},
     pages = {633--639},
     publisher = {mathdoc},
     volume = {6},
     number = {5},
     year = {1969},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1969_6_5_a14/}
}
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I. T. Kiguradze. Conditions for non-oscillation of singular linear differential equations of second order. Matematičeskie zametki, Tome 6 (1969) no. 5, pp. 633-639. http://geodesic.mathdoc.fr/item/MZM_1969_6_5_a14/