Lyapunov-type inequality for a class of quasilinear systems

Yang, Xiao‐Jun; Kim, Young Dong; Lo, Kueiming

doi:10.1016/j.mcm.2010.11.083

Cited by 12 publications

(5 citation statements)

References 10 publications

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“…The results in this section are based on joint work with Pablo de Napoli [36] and Julián Fernández Bonder [48], and several recent articles generalizing those results; see, for instance, [15,16,108,115]. Let (u, v) be the eigenpair associated to the first eigenvalue λ 1 of the following system,…”

Section: Resonant Systemsmentioning

confidence: 99%

Lyapunov-type Inequalities

Pinasco

2013

SpringerBriefs in Mathematics

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SpringerBriefs in MathematicsThis work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher's location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein.Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) To Ceci, Fede, and Selva Preface I used to think that the Sturm-Liouville theory of second-order ordinary differential equations was one of the most beautiful areas of mathematics. Its simplicity, together with the power of the comparison and oscillation theorems, shed a different light on second-order ordinary differential equations. However, while reading a transcription of a talk of G.C. Rota, I realized something: there are many interesting problems, both of theoretical and applied origin, that cannot be analyzed with the Sturmian tools.Take the unit ball in R N : just the simple reduction to polar coordinates introduces the coefficient r N−1 , which vanishes at the origin and is bounded above by 1, for all N. Moreover, Bessel, Hermite, Legendre, . . . , almost all the special families of functions that appear as eigenfunctions of second-order ordinary differential operators, are indeed eigenfunctions of singular or degenerate operators, and the Sturmian arguments fail. What can we do now?If we write the Sturmian bounds in modern notation, we are using the L ∞ norm of the weight, and what happens if we change it to another norm, say L 1 ? Indeed, the answer is known, and it is rela...

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Section: Resonant Systemsmentioning

confidence: 99%

Lyapunov-type Inequalities

Pinasco

2013

SpringerBriefs in Mathematics

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“…A thorough literature review of continuous and discrete Lyapunov-type inequalities and their applications can be found in the survey article by Cheng [3]. Some other recent related results can be found in the articles [4][5][6][7][8][9][10][11][12][13][14].…”

Section: (T) + Q(t)x(t)mentioning

confidence: 99%

Lyapunov-type inequalities for a class of even-order differential equations

Zhang

2012

J Inequal Appl

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“…The half linear version of Lyapunov inequality was obtained in [5][6][7][8][9]. To the best of our knowledge, although many results have been obtained for quasilinear systems [10][11][12][13][14][15][16][17][18][19][20][21][22][23], there is little known for the impulsive quasilinear systems [24]. Although there is a large body of literature on quasilinear systems that we can not cover completely, the results in [10,11,24] and in [22] are worth mentioning due to their contribution to these subject.…”

Section: Introductionmentioning

confidence: 99%

Lyapunov type inequalities and their applications for quasilinear impulsive systems

Kayar

2019

Journal of Taibah University for Science

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A novel Lyapunov-type inequality for Dirichlet problem associated with the quasilinear impulsive system involving the (p j , q j )-Laplacian operator for j = 1,2 is obtained. Then utility of this new inequality is exemplified in finding disconjugacy criterion, obtaining lower bounds for associated eigenvalue problems and investigating boundedness and asymptotic behaviour of oscillatory solutions. The effectiveness of the obtained disconjugacy criterion is illustrated via an example. Our results not only improve the recent related results but also generalize them to the impulsive case.

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Lyapunov-type inequality for a class of quasilinear systems

Cited by 12 publications

References 10 publications

Lyapunov-type Inequalities

Lyapunov-type Inequalities

Lyapunov-type inequalities for a class of even-order differential equations

Lyapunov type inequalities and their applications for quasilinear impulsive systems

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