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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
DOI: https://doi.org/10.1090/S0002-9939-1978-0481246-1
MathSciNet review: 0481246
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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.


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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