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Some Oscillation Theorems for Higher Order Linear Differential Equations with Entire Coefficients of Small Growth

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Abstract

We show that if A and B are entire of order less than 1/6, and are not both polynomials, then the linear differential equation

$y(3)+Ay^\prime+By=0$

can never have a fundamental set of solutions each having zeros with finite exponent of convergence. We go on to consider higher order equations where one coefficient is dominant in the sense that either it has larger order than any other coefficient, or it is the only transcendental coefficient.

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Authors and Affiliations

  1. Department of Mathematics, University of Nottingham, Nottingham, NG7 2RD

    J. K. Langley

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  1. J. K. Langley
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Langley, J.K. Some Oscillation Theorems for Higher Order Linear Differential Equations with Entire Coefficients of Small Growth. Results. Math. 20, 517–529 (1991). https://doi.org/10.1007/BF03323190

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  • DOI: https://doi.org/10.1007/BF03323190

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