Playing Around Resonance
An Invitation to the Search of Periodic Solutions for Second Order Ordinary Differential Equations

Authors: Alessandro Fonda



Provides an up-to-date description of nonlinear boundary value problems

Theory of periodic solutions of ODEs are treated

Permits to fastly reach advanced scientific results and open problems in the field

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

Front Matter
Pages i-xvi

Preliminaries on Hilbert Spaces
Pages 1-29

Operators in Hilbert Spaces
Pages 31-45

The Semilinear Problem
Pages 47-70

The Topological Degree
Pages 71-99

Nonresonance and Topological Degree
Pages 101-135

Playing Around Resonance
Pages 137-156

The Variational Method
Pages 157-171

At Resonance, Again
Pages 173-191

Lusternik–Schnirelmann Theory
Pages 193-212

The Poincaré–Birkhoff Theorem
Pages 213-229

A Myriad of Periodic Solutions
Pages 231-254

Back Matter
Pages 255-309

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