A general result regarding the growth of solutions of first-order differential equations
Author:
Steven B. Bank
Journal:
Proc. Amer. Math. Soc. 71 (1978), 39-45
MSC:
Primary 34C10
DOI:
https://doi.org/10.1090/S0002-9939-1978-0481246-1
MathSciNet review:
0481246
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Abstract | References | Similar Articles | Additional Information
Abstract: In this paper, we treat first-order algebraic differential equations whose coefficients are arbitrary complex-valued functions on an interval , and we obtain an estimate on the growth of all real-valued solutions on
. Our result includes, as a very special case, the well-known result of Lindelöf for polynomial coefficients.
- [1] S. Bank, Some results on analytic and meromorphic solutions of algebraic differential equations, Advances in Math. 15 (1975), 41-62. MR 0379940 (52:844)
- [2] R. Bellman, Stability theory of differential equations, Dover, New York, 1953. MR 0061235 (15:794b)
- [3] K. Cooke, The rate of increase of real continuous solutions of algebraic differential-difference equations of the first order, Pacific J. Math. 4 (1954), 483-501. MR 0065008 (16:371b)
- [4] -, The rate of increase of real continuous solutions of certain algebraic functional equations, Trans. Amer. Math. Soc. 92 (1959), 106-124. MR 0107765 (21:6487)
- [5] O. Lancaster, Some results concerning the behavior at infinity of real continuous solutions of algebraic difference equations, Bull. Amer. Math. Soc. 46 (1940), 169-177. MR 0001108 (1:181e)
- [6] E. Lindelöf, Sur la croissance des intégrales des équations différentielles algébrique du premier ordre, Bull. Soc. Math. France 27 (1899), 205-215. MR 1504345
- [7] S. M. Shah, On real continuous solutions of algebraic difference equations, Bull. Amer. Math. Soc. 53 (1947), 548-558. MR 0022299 (9:189a)
- [8] -, On real continuous solutions of algebraic difference equations. II, Proc. Nat. Inst. Sci. India Sect. A. 16 (1950), 11-17. MR 0036422 (12:105f)
- [9] T. Vijayaraghavan, Sur la croissance des fonctions définies par les équations différentielles, C. R. Acad. Sci. Paris 194 (1932), 827-829.
- [10] T. Vijayaraghavan, N. Basu and S. Bose, A simple example for a theorem of Vijayaraghavan, J. London Math. Soc. 12 (1937), 250-252.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1978-0481246-1
Keywords:
Algebraic differential equations,
growth of solutions
Article copyright:
© Copyright 1978
American Mathematical Society