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The one-dimensional Schrödinger equation with a quasiperiodic potential. (English. Russian original) Zbl 0333.34014

Funct. Anal. Appl. 9, 279-289 (1976); translation from Funkts. Anal. Prilozh. 9, No. 4, 8-21 (1975).

MSC:

34L99 Ordinary differential operators
34F05 Ordinary differential equations and systems with randomness
46N99 Miscellaneous applications of functional analysis
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[2] E. C. Titchmarsh, Eigenfunction Expansions Associated with Second-Order Differential Equations, Oxford University Press (1962). · Zbl 0099.05201
[3] A. M. Dykhne, ”Quasiclassical particle in one-dimensional periodic potential,” Zh. Eksperim. i Teor. Fiz.,40, No. 5, 1423-1426 (1961).
[4] S. G. Simonyan, ”Asymptotic properties of the width of gaps in the spectrum of the Sturm?Liouville operator with a periodic potential,” Differents. Uravnen.,6, No. 7, 1265-1272 (1970).
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[8] N. N. Bogolyubov, Yu. A. Mitropol’skii, and A. M. Samoilenko, Method of Faster Convergence in Nonlinear Mechanics [in Russian], Naukova Dumka, Kiev (1969).
[9] É. G. Belaga, ”Reducibility of systems of ordinary differential equations in the neighborhood of almost periodic motion,” Dokl. Akad. Nauk SSSR,143, No. 2, 255-258 (1962). · Zbl 0117.30503
[10] J. Moser, ”Perturbation theory for almost periodic solutions for nonlinear differential equations,” Intern. Symposium Nonlinear Differential Equations and Nonlinear Mechanics, Academic Press, New York (1963). · Zbl 0132.32305
[11] J. Moser, ”A new technique for the construction of solutions of nonlinear differential equations,” Proc. National Academy of Sci. USA,47 (1961). · Zbl 0104.30503
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