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Sibirsk. Mat. Zh., 2012, Volume 53, Number 4, Pages 862–873 (Mi smj2369)  

Generalized Lyapunov inequalities involving critical Sobolev exponents

H. J. Kwona, S. A. Timoshinb

a Department of Mathematics and PMI, POSTECH, Pohang, Kyungbuk, Republic of Korea
b Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences, Irkutsk

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.

Keywords: elliptic equations, critical exponent, Lyapunov inequality.

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English version:
Siberian Mathematical Journal, 2012, 53:4, 691–701

Bibliographic databases:

UDC: 517.954
Received: 07.06.2011

Citation: H. J. Kwon, S. A. Timoshin, “Generalized Lyapunov inequalities involving critical Sobolev exponents”, Sibirsk. Mat. Zh., 53:4 (2012), 862–873; Siberian Math. J., 53:4 (2012), 691–701

Citation in format AMSBIB
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\paper Generalized Lyapunov inequalities involving critical Sobolev exponents
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\pages 862--873
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