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Sibirskii Matematicheskii Zhurnal, 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
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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.
Keywords: elliptic equations, critical exponent, Lyapunov inequality.
Received: 07.06.2011
English version:
Siberian Mathematical Journal, 2012, Volume 53, Issue 4, Pages 691–701
DOI: https://doi.org/10.1134/S0037446612040118
Bibliographic databases:
Document Type: Article
UDC: 517.954
Language: Russian
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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