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On Properties of Third-Order Differential Equations via Comparison Principles

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  • B. Baculíková
  • J. Džurina

Abstract

The objective of this paper is to offer sufficient conditions for certain asymptotic properties of the third-order functional differential equation [ ð ‘Ÿ ( ð ‘¡ ) [ ð ‘¥ ′ ( ð ‘¡ ) ] ð ›¾ ] î…ž î…ž + ð ‘ ( ð ‘¡ ) ð ‘¥ ( ð œ ( ð ‘¡ ) ) = 0 , where studied equation is in a canonical form, that is, ∫ ∞ ð ‘Ÿ − 1 / ð ›¾ ( ð ‘ ) d ð ‘ = ∞ . Employing Trench theory of canonical operators, we deduce properties of the studied equations via new comparison theorems. The results obtained essentially improve and complement earlier ones.

Suggested Citation

  • B. Baculíková & J. Džurina, 2012. "On Properties of Third-Order Differential Equations via Comparison Principles," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-10, July.
  • Handle: RePEc:hin:jijmms:975298
    DOI: 10.1155/2012/975298
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