Linear differential equations with interval spectrum

Author:
Russell A. Johnson

Journal:
Proc. Amer. Math. Soc. **80** (1980), 90-94

MSC:
Primary 34C10; Secondary 54H20

DOI:
https://doi.org/10.1090/S0002-9939-1980-0574514-5

MathSciNet review:
574514

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let *E* be the set of equations in the hull of a fixed two-dimensional, almost-periodic, linear differential equation with interval spectrum which admit a bounded solution. Among other things, we prove that *E* is of first category and of measure zero.

**[1]**R. Ellis,*Lectures on topological dynamics*, Benjamin, New York, 1969. MR**0267561 (42:2463)****[2]**R. Johnson,*Ergodic theory and linear differential equations*, J. Differential Equations**28**(1978), 23-34. MR**487484 (80c:34044)****[3]**-,*Minimal functions with unbounded integral*, Israel J. Math.**31**(1978), 133-141. MR**516249 (80g:54047)****[4]**V. M. Millionščikov,*Proof of the existence of irregular systems of linear differential equations with almost periodic coefficients*, Differential Equations**4**(1968), 203-205. MR**0229912 (37:5478)****[5]**-,*A proof of the existence of nonregular systems of linear differential equations with quasiperiodic coefficients*, Differential Equations**5**(1969), 1475-1478. MR**0257477 (41:2127)****[6]**-,*Statistically regular systems*, Math. USSR-Sb.**4**(1968), 125-135.**[7]**V. V. Nemytski and V. V. Stepanov,*Qualitative theory of differential equations*, English translation, Princeton Math. Series, no. 22, Princeton Univ. Press, Princeton, N. J., 1960. MR**0121520 (22:12258)****[8]**R. J. Sacker and G. R. Sell,*Existence of the dichotomies and invariant splittings for linear differential systems*. I, J. Differential Equations**15**(1974), 429-458. MR**0341458 (49:6209)****[9]**-,*A spectral theory for linear differential systems*, J. Differential Equations**27**(1978), 320-358. MR**0501182 (58:18604)****[10]**G. R. Sell,*Linear differential systems*, Lecture notes, University of Minnesota, 1975.**[11]**W. A. Veech,*Point-distal flows*, Amer. J. Math.**92**(1970), 205-242. MR**0267560 (42:2462)****[12]**R. E. Vinograd,*A problem suggested by N. P. Erugin*, Differential Equations**11**(1975), 474-478. MR**0473360 (57:13028)**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
34C10,
54H20

Retrieve articles in all journals with MSC: 34C10, 54H20

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1980-0574514-5

Article copyright:
© Copyright 1980
American Mathematical Society