Geodesic
Oscillation and Comparison Theorems for Second Order Linear Differential Equations with Integrable Coefficients
Canadian journal of mathematics, Tome 26 (1974) no. 2, pp. 294-301

Voir la notice de l'article provenant de la source Cambridge University Press

The classical comparison and interlacing theorems of Sturm were originally proved for the equations under the assumption that all coefficients are real-valued, continuous, and p > 0, P > 0. Atkinson [1, Chapter 8] has carried out the standard theory for eigenvalue problems involving (1), under the more general hypothesis 
Butler, G.; Macki, J. W. Oscillation and Comparison Theorems for Second Order Linear Differential Equations with Integrable Coefficients. Canadian journal of mathematics, Tome 26 (1974) no. 2, pp. 294-301. doi: 10.4153/CJM-1974-031-8
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[1] 1. Atkinson, F. V., Discrete and continuous boundary problems (Academic Press, New York, 1964). Google Scholar

[2] 2. Cafiero, F., Su un problema ai limiti relativo alVequazione y′ = f(x, y,), Giorn. Mat. Battaglini 77 (1947), 145–163. Google Scholar

[3] 3. Diaz, J. B. and McLaughlin, J. R., Sturm separation and comparison theorems for ordinary and partial differential equations, Atti Accad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez. I, Series VIII, IX (1969), No. 5, 136–194. Google Scholar

[4] 4. Hartman, P., Ordinary differential equations (Wiley, New York, 1964). Google Scholar

[5] 5. Jakubovic, V. A., Oscillatory properties of the solutions of canonical equations, Mat. Sb. 56 (1962), 3–42; Amer. Math. Soc. Transi. 42 (1964), 247–288. Google Scholar

[6] 6. Kiasnosel'skii, M. A., Percov, A. I., Provolockii, A. I., and Zabreiko, P. P., Plane vector fields (Academic Press, New York, 1966). Google Scholar

[7] 7. Muldowney, J. S., On an inequality of Peano, Can. Math. Bull. 16 (1973), 79–82. Google Scholar

[8] 8. Reid, W. T., Some remarks on special disconjugacy criteria for differential systems, Pacific J. Math. 35 (1970), 763–772. Google Scholar

[9] 9. Reid, W. T., Generalized linear differential systems, J. Math. Mech. 8 (1959), 705–726. Google Scholar

[10] 10. Reid, W. T., Ordinary differential equations (Wiley, New York, 1971). Google Scholar

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