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On solutions of functional-differential equations f′(x) = a(x)f(g(x)) + b(x)f(x) + c(x) in the large

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Abstract

We consider solutions of functional-differential equations

$$f'(x) = a(x)f(g(x)) + b(x)f(x) + c(x)$$

in both real and complex variables. We characterize entire solutions g when f is a meromorphic function in the complex plane and a ≠ 0, b, c are constants or polynomials. We also examine questions of existence and uniqueness of the solutions in the real variable for initial value problems and provide theorems that are valid “in the large”.

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Authors and Affiliations

  1. Department of Mathematics, Florida International University, Miami, FL, 33199, USA

    Bao Qin Li

  2. Department of Mathematics and Statistics, Notre Dame University, Louaize, Lebanon

    Elias G. Saleeby

Authors
  1. Bao Qin Li
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  2. Elias G. Saleeby
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Correspondence to Bao Qin Li.

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Qin Li, B., Saleeby, E.G. On solutions of functional-differential equations f′(x) = a(x)f(g(x)) + b(x)f(x) + c(x) in the large. Isr. J. Math. 162, 335–348 (2007). https://doi.org/10.1007/s11856-007-0101-z

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  • DOI: https://doi.org/10.1007/s11856-007-0101-z

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