On an oscillation criterion of Hartman, Wintner and Potter

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1. Breuer S., Gottlieb D., Separation of roots and oscillation in ordinary linear differential equations of second order, Proc. Amer. Math. Soc. 29 (1971), 487-493. (1971) Zbl0224.34024MR0276545
2. Caratheodory C., Vorlesungen über reelle Funktionen, 2. Aufl. Teubner Leipzig 1927. (1927) 
3. Etgen G. J., Pawlowski J. F., Oscillation criteria for second order self adjoint differential systems, Pacific J. Math. 66 (1976) 99-110. (1976) Zbl0355.34017MR0440147
4. Fite W. B., Concerning the zeros of the solutions of certain differential equations, Trans. Amer. Math. Soc. 19 (1917), 341-352. (1917) MR1501107
5. Gagliardo E., Sul comportamento asintotico degli integrali dell’equazione differenziale $y"+A\left(x\right)y=0$ con $A\left(x\right)\ge 0$, Boll. Unione Mat. Ital. (3) 8 (1953), 177-185. (1953) MR0056779
6. Guggenheimer H., Hill equations with coexisting periodic solutions, J. Diff. Equations 5 (1969), 159-166. (1969) Zbl0186.41003MR0239193
7. Hartman P., Wintner A., On non-conservative linear oscillators of low frequency, Amer. J. Math. 70 (1948), 529-539. (1948) Zbl0037.19002MR0026736
8. Kreith K., Oscillation theory, Lecture Notes in Math. 324, Springer-Verlag Berlin, Heidelberg, New York 1973. (1973) Zbl0258.35001
9. Laugwitz D., Differentialgeometrie in Vektorräumen, Vieweg Braunschweig 1965. (1965) Zbl0139.14904MR0182924
10. Leighton W., Principal quadratic functionals and self adjoint second-order differential equations, Proc. Nat. Acad. Sci. 35 (1949) 192-193. (1949) Zbl0032.34603MR0030672
11. Leighton W., On self adjoint differential equations of second order, J. London Math. Soc. 27 (1952), 37-47. (1952) Zbl0048.06503MR0046506
12. Moore R. A., The behavior of solutions of a linear differential equation of second order, Pacific J. Math. 5 (1955), 125-145. (1955) MR0068690
13. Neuman F., Centroaffine invariants of plane curves in connection with the theory of the second order linear differential equations, Archivum Math. (Brno) 4 (1968), 201-216. (1968) Zbl0218.34007MR0267512
14. Opial Z., Sur une critère d’oscillation des integrales de l’equation différentielle ${\left(Q\left(t\right)x^{\text{'}}\right)}^{\text{'}}+f\left(t\right)x=0$, Ann. Polon. Math. 6 (1959/1960), 99-104. (1959) MR0104876
15. Pfaff R., Zur Theorie der gewöhnlichen linearen Differentialgleichung zweiter Ordnung mit Distributionskoeffizient, Dissertation Darmstadt 1978. (1978) MR0481259
16. Potter R. L., On self-adjoint differential equations of second order, Pacific J. Math. 3 (1953),. 467-491. (1953) Zbl0051.06502MR0056156
17. Ráb M., Kriterien für die Oszillation der Lösungen der Differentialgleichung ${\left[p\left(x\right)y^{\text{'}}\right]}^{\text{'}}+q\left(x\right)y=0$, Časopis Pěst. Mat. 84 (1959), 335-370. (1959) MR0114964
18. Swanson C. A., Comparison and oscillation theory of linear differential equations, Academic Press New York, London 1968. (1968) Zbl0191.09904MR0463570
19. Willet D., Classification of second order linear differential equations with respect to oscillation, In: Lectures on ordinary differential equations. Ed. R. McKelvey, Academic Press New York, London 1970. (1970) MR0280800
20. Wintner A., A criterion of oscillatory stability, Quarterly Appl. Math. 7 (1949), 115-117. (1949) Zbl0032.34801MR0028499