Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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
MathSciNet review: 0481246
Full-text PDF Free Access

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 $ [{x_0}, + \infty )$, and we obtain an estimate on the growth of all real-valued solutions on $ [{x_0}, + \infty )$. Our result includes, as a very special case, the well-known result of Lindelöf for polynomial coefficients.


References [Enhancements On Off] (What's this?)

  • [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.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34C10

Retrieve articles in all journals with MSC: 34C10


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