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Generalized Lyapunov inequalities involving critical Sobolev exponents

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Abstract

We consider Lyapunov-type inequalities generalizing the famous inequality that gives a necessary condition for the existence of solutions to a boundary value problem for a second order ordinary differential equation. For certain critical cases, when the inequalities are strict, we study the asymptotic behavior of minimizing sequences.

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Authors and Affiliations

  1. PMI, Pohang Kyungbuk, Republic of Korea

    H. J. Kwon

  2. Institute of Systems Dynamics and Control Theory, Irkutsk, Russia

    S. A. Timoshin

Authors
  1. H. J. Kwon
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  2. S. A. Timoshin
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Correspondence to S. A. Timoshin.

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Original Russian Text Copyright © 2012 Kwon H.J. and Timoshin S.A.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 53, No. 4, pp. 862–873, July–August, 2012.

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Kwon, H.J., Timoshin, S.A. Generalized Lyapunov inequalities involving critical Sobolev exponents. Sib Math J 53, 691–701 (2012). https://doi.org/10.1134/S0037446612040118

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  • DOI: https://doi.org/10.1134/S0037446612040118

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