Playing Around Resonance - Alessandro Fonda

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Résumé :
This book provides an up-to-date description of the methods needed to face the existence of solutions to some nonlinear boundary value problems. All important and interesting aspects of the theory of periodic solutions of ordinary differential equations related to the physical and mathematical question of resonance are treated. The author has chosen as a model example the periodic problem for a second order scalar differential equation. In a paedagogical style the author takes the reader step by step from the basics to the most advanced existence results in the field....

Biographie:
Alessandro Fonda obtained his PhD at the International School for Advanced Studies (SISSA-Trieste) in 1988, under the supervision of Jean Mawhin. Then he first got a research position in Belgium, before going back to Italy, at the University of Trieste, becoming full professor in 2002. He obtained two prizes from the Acad?mie Royale de Belgique for his monographs Periodic solutions of scalar second order differential equations with a singularity in 1993 and Playing around resonance. An invitation to the search of periodic solutions for second order ordinary differential equations in 2017. He has been invited to give plenary lectures at several conferences in Europe and in the USA. His research interests are mainly concentrated on existence and multiplicity problems for boundary value problems. He recently gave an important contribution to the study of the periodic problem for Hamiltonian systems by providing some generalizations of the Poincar?-Birkhoff Theorem in higher dimensions. He also studied problems related to differential inclusions, persistence in dynamical systems, and global behaviour of the solutions to planar systems....

Sommaire:

1.Preliminaries on Hilbert spaces.- 2.Operators in Hilbert spaces.- 3.The semilinear problem.- 4.The topological degree.- 5.Nonresonance and topological degree.- 6.Playing around resonance.- 7.The variational method.- 8.At resonance, again.- 9.Lusternik-Schnirelmann theory. 10.The Poincar?-Birkhoff theorem.- 11.A myriad of periodic solutions.