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On a problem of Hartman and Wintner

  • N. Chernyavskaya (a1)

Abstract

The Hartman–Wintner problem on asymptotic equivalence of fundamental systems of solutions (FSSs) for two Sturm–Liouville equations is studied. The following results are obtained: a criterion of asymptotic equivalence of FSSs, and sufficient conditions of asymptotic equivalence of FSSs which are expressed in terms of the coefficients of the considered equations only.

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1Chen, S.. Asymptotic integration of nonoscillatory second order differential equations. Trans. Amer. Math. Soc. 327 (1991), 853–65.
2Chen, S.. Asymptotic integration of the principal solution of a second-order differential equation. Bull. London Math. Soc. 23 (1991), 457–64.
3Chernyavskaya, N. and Shuster, L.. WKB-approximations from the perturbation theory viewpoint. Oper. Theory Adv. Appl. 46 (1990), 119–23.
4Chernyavskaya, N. and Shuster, L.. On a representation of the solutions of the Sturm–Liouville equation and its applications. Differentsial'nye Uravneniya 28 (1992), 537–40.
5Chernyavskaya, N. and Shuster, L.. Estimates for Green's function of the Sturm–Liouville operator. J. Differential Equations 111 (1994), 410–20.
6Davies, E. B. and Harrell, E. M.. Conformally fiat Riemannian metrics, Schrödinger operators and semiclassical approximation. J. Differential Equations 66 (1987), 165–88.
7Eastham, M. S. P.. The Asymptotic Solution of Linear Differential Systems. Applications of the Levinson Theorem (Oxford: Clarendon Press, 1989).
8Fedorjuk, M. V.. Asymptotic Methods for Linear Ordinary Differential Equations (Moscow: Nauka, 1983).
9Hartman, P.. Ordinary Differential Equations (New York: Wiley, 1964).
10Mynbaev, K. and Otelbaev, M.. Weighted Functional Spaces and Differential Operator Spectrum (Moscow: Nauka, 1988).
11Olver, F. W. J.. Asymptotics and Special Functions (New York: Academic Press, 1974).
12Shuster, L.. A priori properties of solutions of a Sturm–Liouville equation and A. M. Molchanov 's criterion. Math. Notes Acad. Sci USSR 50 (1991), 746–51 (translation of Mat. Zametki).
13Šimš, J.. Asymptotic integration of a second-order ordinary differential equation. Proc. Amer. Math. Soc. 101 (1987), 96100.
14Steklov, W. A.. Sur une méthode nouvelle pour resoudre plusieurs problèmes sur le développement d'une fonction arbitraire en séries infinies. C. R. Acad. Sci. Paris 144 (1907), 1329–32.
15Trench, W. F.. Linear perturbations of a nonoscillatory second order equation. Proc. Amer. Math. Soc. 97 (1986), 423–8.

On a problem of Hartman and Wintner

  • N. Chernyavskaya (a1)

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