The Maslov Index and Global Bifurcation for Nonlinear Boundary Value Problems

We first describe the notion of Maslov index and relate it to the concepts of moment of verticality and of phase-angles. We then illustrate the role of the Maslov index in the development of global bifurcation results for nonlinear first order differentia

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Fondazione C.I.M.E., Firenze C.I.M.E. stands for Centro Internazionale Matematico Estivo, that is, International Mathematical Summer Centre. Conceived in the early fifties, it was born in 1954 in Florence, Italy, and welcomed by the world mathematical community: it continues successfully, year for year, to this day. Many mathematicians from all over the world have been involved in a way or another in C.I.M.E.’s activities over the years. The main purpose and mode of functioning of the Centre may be summarised as follows: every year, during the summer, sessions on different themes from pure and applied mathematics are offered by application to mathematicians from all countries. A Session is generally based on three or four main courses given by specialists of international renown, plus a certain number of seminars, and is held in an attractive rural location in Italy. The aim of a C.I.M.E. session is to bring to the attention of younger researchers the origins, development, and perspectives of some very active branch of mathematical research. The topics of the courses are generally of international resonance. The full immersion atmosphere of the courses and the daily exchange among participants are thus an initiation to international collaboration in mathematical research. C.I.M.E. Director Pietro ZECCA Dipartimento di Energetica “S. Stecco” Universit`a di Firenze Via S. Marta, 3 50139 Florence Italy e-mail: [email protected]

C.I.M.E. Secretary Elvira MASCOLO Dipartimento di Matematica “U. Dini” Universit`a di Firenze viale G.B. Morgagni 67/A 50134 Florence Italy e-mail: [email protected]

For more information see CIME’s homepage: http://www.cime.unifi.it CIME activity is carried out with the collaboration and financial support of: - INdAM (Istituto Nazionale di Alta Matematica) - MIUR (Ministero dell’Universita’ e della Ricerca)

Anna Capietto  Peter Kloeden Sylvia Novo  Rafael Ortega



Jean Mawhin

Stability and Bifurcation Theory for Non-Autonomous Differential Equations Cetraro, Italy 2011 Editors: Russell Johnson Maria Patrizia Pera

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Anna Capietto Universit`a di Torino Dipartimento di Matematica Torino, Italy Peter Kloeden Universit¨at Frankfurt Institut f¨ur Mathematik Frankfurt, Germany

Sylvia Novo E. de Ingenier´ıas Industriales Departamento de Matem´atica Aplicada Universidad de Valladolid Valladolid, Spain Rafael Ortega Universidad de Granada Departamento de Matem´atica Aplicada Granada, Spain

Jean Mawhin Universit´e Catholique de Louvain Institut de Recherche en Math´ematique et Physique Louvain-la-Neuve, Belgium

ISBN 978-3-642-32905-0 ISBN 978-3-642-32906-7 (eBook) DOI 10.1007/978-3-642-32906-7 Springer Heidelberg New York Dordrecht London Lecture Notes in Mathematics ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 Library of Congress Control Number: 2012951625 Mathematics Subject Classification (2010): 34B15, 37B55, 34C25, 37E40, 37G35, 34K12 c Springer-Verlag Berlin Heidelberg 2013  This work is subject to