Positive Solutions to Indefinite Problems: A Topological Approach (Frontiers in Mathematics) - Softcover

Feltrin, Guglielmo

Softcover

ISBN 10: 3319942379 ISBN 13: 9783319942377

Publisher: Birkhäuser, 2018

Synopsis

This book is devoted to the study of positive solutions to indefinite problems. The monograph intelligibly provides an extensive overview of topological methods and introduces new ideas and results. Sticking to the one-dimensional setting, the author shows that compelling and substantial research can be obtained and presented in a penetrable way.

In particular, the book focuses on second order nonlinear differential equations. It analyzes the Dirichlet, Neumann and periodic boundary value problems associated with the equation and provides existence, nonexistence and multiplicity results for positive solutions. The author proposes a new approach based on topological degree theory that allows him to answer some open questions and solve a conjecture about the dependence of the number of positive solutions on the nodal behaviour of the nonlinear term of the equation. The new technique developed in the book gives, as a byproduct, infinitely many subharmonic solutions and globally defined positive solutions with chaotic behaviour. Furthermore, some future directions for research, open questions and interesting, unexplored topics of investigation are proposed.

About this title

From the Back Cover

This book is devoted to the study of positive solutions to indefinite problems. The monograph intelligibly provides an extensive overview of topological methods and introduces new ideas and results. Sticking to the one-dimensional setting, the author shows that compelling and substantial research can be obtained and presented in a penetrable way.

In particular, the book focuses on second order nonlinear differential equations. It analyzes the Dirichlet, Neumann and periodic boundary value problems associated with the equation and provides existence, nonexistence and multiplicity results for positive solutions. The author proposes a new approach based on topological degree theory that allows him to answer some open questions and solve a conjecture about the dependence of the number of positive solutions on the nodal behaviour of the nonlinear term of the equation. The new technique developed in the book gives, as a byproduct, infinitely many subharmonic solutions andglobally defined positive solutions with chaotic behaviour. Furthermore, some future directions for research, open questions and interesting, unexplored topics of investigation are proposed.

Edition details

• Publisher: Birkhäuser
• Publication date: 2018
• Language: English
• ISBN 10: 3319942379
• ISBN 13: 9783319942377
• Binding: Paperback
• Edition number: 1
• Number of pages: 333