Oscillation on Finite or Infinite Intervals of Second Order Linear Differential Equations(1)
Canadian mathematical bulletin, Tome 14 (1971) no. 4, pp. 539-550

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

Recently, Ronveaux [11] has shown how to use a combination of a Riccati transformation and a homographie transformation to estimate both from below and above the distance between a zero and the succeeding or preceding extremum (zero of y' ) of solutions of 1.1 In this paper, we show how such transformations can be used to derive an equation from which the distance between successive zeros of a solution y of (1.1) can be estimated directly.
Willett, D. Oscillation on Finite or Infinite Intervals of Second Order Linear Differential Equations(1). Canadian mathematical bulletin, Tome 14 (1971) no. 4, pp. 539-550. doi: 10.4153/CMB-1971-096-8
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[1] 1. Banks, D., Bounds for eigenvalues and generalized convexity, Pacific J. Math. 13 (1963), 1031-1052. Google Scholar

[2] 2. Elbert, A., On the solutions of the differential equation y"+q(x)y = 0, where [q(x)]γ is concave, II, Studia Sci. Math. Hung. 4 (1969), 257-266. Google Scholar

[3] 3. Fink, A. M., On the zeros of y"+py = Q with linear, convex, and concave p, J. Math. Pures Appl. 46 (1967), 1-10. Google Scholar

[4] 4. Fink, A. M. and Mary, D. F. St., On an inequality of Nehari, Proc. Amer. Math. Soc. 21 (1969), 640-642. Google Scholar

[5] 5. Galbraith, A., On the zeros of solutions of ordinary differential equations of the second order, Proc. Amer. Math. Soc. 17 (1966), 333-337. Google Scholar

[6] 6. Hartman, P. and Wintner, A., On an oscillation criterion of Lyapunov, Amer. J. Math. 73 (1951), 885–890. Google Scholar

[7] 7. Hartman, P. and Wintner, A., On an oscillation criterion of de la Vallée Poussin, Quart. Appl. Math. 13 (1955), 330-332. Google Scholar

[8] 8. Lyapunov, A., Sur une série relative à la théorie des équations différentielles linéaires à coefficient périodiques, C.R. Acad. Sci. Paris, 123 (1896), 1248-1252. Google Scholar

[9] 9. Opial, Z., Sur les intégrales oscillantes de l'équation différentielle u"+f(t)u = 0, Ann. Polon. Math. 4 (1958), 308-313. Google Scholar

[10] 10. Opial, Z., Sur une inégalité de C. de la Vallée Poussin dans la théorie de l'équation différentielle linéaire du second ordre, Ann. Polon. Math. 6 (1959–60), 87-91. Google Scholar

[11] 11. Ron veaux, A., Equations différentielles du second ordre: distances entre zéro et extremum des solutions, Ann. Soc. Sci. Bruxelles Sér. I, 84 (1970), 5-20. Google Scholar

[12] 12. de la Vallée Poussin, C., Sur l'équation différentielle linéaire du second ordre, J. Math. Pures Appl. 8 (1929), 125-144. Google Scholar

[13] 13. Willett, D., Classification of second order linear differential equations with respect to oscillation, Advances in Math. 3 (1969), 594-623. Google Scholar

[14] 14. Willett, D., A necessary and sufficient condition for the oscillation of some linear second order differential equations, Rocky Mt. Math. J. 1 (1970), 357-365. Google Scholar

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