Playing Around Resonance

An Invitation to the Search of Periodic Solutions for Second Order Ordinary Differential Equations
1. Auflage 2016
ISBN: 978-3-319-47089-4
Verlag: Springer International Publishing

Buch, Englisch, 309 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 6151 g

Reihe: Birkhäuser Advanced Texts Basler Lehrbücher

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.

Zielgruppe

Upper undergraduate

Autoren/Hrsg.

Fonda, Alessandro

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

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 Poincaré-Birkhoff theorem.- 11.A myriad of periodic solutions.