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Positive Solutions with Nonpower Asymptotic Behavior and Quasiperiodic Solutions to an Emden–Fowler Type Higher Order Equations

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We consider the differential equation y (n) = p 0|y|k sgn y, where p 0 > 0 and 12 ≤ n ≤ 14, and prove that there exists k > 1 such that the equation has positive solutions with nonpower asymptotics y(x) = (x ∗ -x)-α h(ln (x ∗ -x)), x < x ∗ , where h is a nonconstant continuous positive periodic function. For n ≥ 2 we prove that such a solution exists, but with an oscillating periodic function h. Bibliography: 8 titles. Illustrations: 1 figure.

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References

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  1. Lomonosov Moscow State University, Moscow, 119991, Russia

    I. V. Astashova

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  1. I. V. Astashova
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Correspondence to I. V. Astashova.

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Translated from Problemy Matematicheskogo Analiza 79, March 2015, pp. 9–23.

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Astashova, I.V. Positive Solutions with Nonpower Asymptotic Behavior and Quasiperiodic Solutions to an Emden–Fowler Type Higher Order Equations. J Math Sci 208, 8–23 (2015). https://doi.org/10.1007/s10958-015-2419-0

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