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A note on the existence and asymptotic behavior of nonoscillatory solutions of fourth order quasilinear differential equations

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Abstract

This paper is concerned with nonoscillatory solutions of the fourth order quasilinear differential equation

$$(p(t)\left| {u''} \right|^{\alpha - 1} u'')'' + q(t)\left| u \right|^{\beta - 1} u = 0,$$

where α > 0, β > 0 and p(t) and q(t) are continuous functions on an infinite interval [a,∞) satisfying p(t) > 0 and q(t) > 0 (t≥a). The growth bounds near t = ∞ of nonoscillatory solutions are obtained, and necessary and sufficient integral conditions are established for the existence of nonoscillatory solutions having specific asymptotic growths as t→∞.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Faculty of Science, Ehime University, Matsuyama, 790-8577, Japan

    Manabu Naito

  2. Department of Mathematics, Northeast Normal University Changchun, Jilin, 130024, China

    Fentao Wu

Authors
  1. Manabu Naito
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  2. Fentao Wu
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Naito, M., Wu, F. A note on the existence and asymptotic behavior of nonoscillatory solutions of fourth order quasilinear differential equations. Acta Mathematica Hungarica 102, 177–202 (2004). https://doi.org/10.1023/B:AMHU.0000023215.24975.ee

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