Playing around resonance : an invitation to the search of periodic solutions for second order ordinary differential equations
Author(s)
Bibliographic Information
Playing around resonance : an invitation to the search of periodic solutions for second order ordinary differential equations
（Birkhäuser advanced texts : Basler Lehrbücher / edited by Herbert Amann, Hanspeter Kraft）
Birkhäuser , Springer, c2016
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Note
Includes bibliographical references (p. 297-305) and index
Description and Table of Contents
Description
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.
Table of Contents
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 Poincare-Birkhoff theorem.- 11.A myriad of periodic solutions.
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