A general result regarding the growth of solutions of first-order differential equations
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- by Steven B. Bank PDF
- Proc. Amer. Math. Soc. 71 (1978), 39-45 Request permission
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
- Steven B. Bank, Some results on analytic and meromorphic solutions of algebraic differential equations, Advances in Math. 15 (1975), 41–62. MR 379940, DOI 10.1016/0001-8708(75)90124-3
- Richard Bellman, Stability theory of differential equations, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1953. MR 0061235
- K. L. 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 65008
- K. L. Cooke, The rate of increase of real continuous solutions of certain algebraic functional equations, Trans. Amer. Math. Soc. 92 (1959), 106–124. MR 107765, DOI 10.1090/S0002-9947-1959-0107765-8
- Otis E. 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 1108, DOI 10.1090/S0002-9904-1940-07164-2
- E. Lindelöf, Sur la croissance des intégrales des équations différentielles algébriques du premier ordre, Bull. Soc. Math. France 27 (1899), 205–215 (French). MR 1504345
- S. M. Shah, On real continuous solutions of algebraic difference equations, Bull. Amer. Math. Soc. 53 (1947), 548–558. MR 22299, DOI 10.1090/S0002-9904-1947-08830-3
- S. M. Shah, On real continuous solutions of algebraic difference equations. II, Proc. Nat. Inst. Sci. India 16 (1950), 11–17. MR 36422 T. Vijayaraghavan, Sur la croissance des fonctions définies par les équations différentielles, C. R. Acad. Sci. Paris 194 (1932), 827-829. T. Vijayaraghavan, N. Basu and S. Bose, A simple example for a theorem of Vijayaraghavan, J. London Math. Soc. 12 (1937), 250-252.
Additional Information
- © Copyright 1978 American Mathematical Society
- 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