Document Zbl 0539.58022

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Boston-London-Melbourne: Pitman Advanced Publishing Program. IV, 350 p. £12.95 (1982).</a> </div> <div class="abstract">The study of stability and bifurcations can be traced back to Euler and the Bernoullis, and that of symmetry at least to Ha眉y; these studies were done in physical situations, not purely mathematical. This book does have examples on circular and cylindrical plates; its emphasis is on pure mathematics, based on the applications. It follows Hilbert’s dictum of concentrating on ”sharper aids and simpler methods”, to generalize, to subsume particular cases and methods into powerful theorems of wide application: the references average one per page and cover a broad range of applications although not all: Aris, Cohen, Cole, Joseph, Koiter and Rosenblat do not feature prominently. <br class="zbmathjax-paragraph">The aim is to examine a set of solutions to an equation dependent on a parameter. The interesting points in such a set are those where uniqueness fails, the bifurcation points. The author does this in the standard way of bifurcation theory. The book covers the main theory for partial differential equations and the symmetry group SO(2), for single and multiple eigenvalues, and with the Lyapunov-Schmidt reduction method. The book is a good review of the author’s own work and that of others over the period to 1981/82.<div class="reviewer"> Reviewer: <a href="/authors/?q=rv%3A3264">J.J.Cross</a></div> <div class="clearfix"></div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A3858028">Cited in <strong>3</strong> Reviews</a></div><div class="clear"><a href="/?q=rf%3A3858028">Cited in <strong>133</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A37G99" title="MSC2020">37G99</a> </td> <td class="space"> Local and nonlocal bifurcation theory for dynamical systems </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A58-02" title="MSC2020">58-02</a> </td> <td class="space"> Research exposition (monographs, survey articles) pertaining to global analysis </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Acircular+and+cylindrical+plates">circular and cylindrical plates</a>; <a href="/?q=ut%3ALyapunov-Schmidt+reduction+method">Lyapunov-Schmidt reduction method</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 0539.58022" data-ciurl="" data-biburl="/bibtex/03858028.bib" data-amsurl="/amsrefs/03858028.bib" data-xmlurl="/xml/03858028.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/03858028.pdf" title="Zbl 0539.58022 as PDF">Review PDF</a> </div> <div class="fulltexts"> </div> <div class="sfx" style="float: right;"> </div> </div> </article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2024 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 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