Geodesic
Disconjugacy Conditions for the Third Order Linear Differential Equation
Canadian mathematical bulletin, Tome 12 (1969) no. 5, pp. 603-613

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An nth order homogeneous linear differential equation is said to be disconjugate on the interval I of the real line in case no non-trivial solution of the equation has more than n - 1 zeros (counting multiplicity) on I. It is the purpose of this paper to establish several necessary and sufficient conditions for disconjugacy of the third order linear differential equation (1.1) where pi(t) is continuous on the compact interval [a, b], i = 0, 1, 2. 
Erbe, Lynn. Disconjugacy Conditions for the Third Order Linear Differential Equation. Canadian mathematical bulletin, Tome 12 (1969) no. 5, pp. 603-613. doi: 10.4153/CMB-1969-078-9
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     author = {Erbe, Lynn},
     title = {Disconjugacy {Conditions} for the {Third} {Order} {Linear} {Differential} {Equation}},
     journal = {Canadian mathematical bulletin},
     pages = {603--613},
     year = {1969},
     volume = {12},
     number = {5},
     doi = {10.4153/CMB-1969-078-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-078-9/}
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