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

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Fonda A. Playing Around Resonance: An Invitation to the Search of Periodic Solutions for Second Order Ordinary Differential Equations
Basel: Birkhäuser, 2016. — 314 p.
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.
Preliminaries on Hilbert Spaces
Operators in Hilbert Spaces
The Semilinear Problem
The Topological Degree
Nonresonance and Topological Degree
Playing Around Resonance
The Variational Method
At Resonance, Again
Lusternik–Schnirelmann Theory
The Poincaré–Birkhoff Theorem
A Myriad of Periodic Solutions
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