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

Format:

Book

Author/Creator:

Fonda, Alessandro., Author.

Series:

Birkhäuser Advanced Texts Basler Lehrbücher, 2296-4894

Language:

English

Subjects (All):

Differential equations.

Differential Equations.

Local Subjects:

Differential Equations.

Physical Description:

1 online resource (XVI, 309 p. 9 illus., 1 illus. in color.)

Edition:

1st ed. 2016.

Place of Publication:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2016.

Summary:

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.

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 Poincaré-Birkhoff theorem

11.A myriad of periodic solutions.

Notes:

Includes bibliographical references and index.

ISBN:

3-319-47090-6