A generalization of Liapunov's inequality
type: Item
instance of: scholarly article
title: A generalization of Liapunov's inequality
zbMATH Open document ID: 0558.34013
DOI: 10.1016/0022-247X(84)90194-X
author: Leon Kotin
published in: Journal of Mathematical Analysis and Applications
publication date: 1984-01-01T00:00:00Z
review text: We consider the boundary value problem \(x''+p(t)x=0\), \(x(0)=x(a)=0\), \(x\not\equiv 0\), and generalize Lyapunov's classical inequality to \(\int^{a}_{0}| p(t)|^{\gamma}dt\geq k_{\gamma}/a^{2\gamma -1}\) for the cases \(\gamma =2,3\), and 3/2. We found the best possible \(k_{\gamma}\) and the optimizing coefficient functions p(t) and corresponding solutions x(t). These results are applied in demonstrating the stability of Hill's equation under suitable conditions.
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 3889924
zbMATH Keywords: Lyapunov disconjugacy
zbMATH Keywords: Lyapunov's inequality
zbMATH Keywords: optimizing coefficient functions
zbMATH Keywords: stability of Hill's equation
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3889924