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Positive solutions to indefinite pro...

Feltrin, Guglielmo.

Positive solutions to indefinite problemsa topological approach /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Positive solutions to indefinite problemsby Guglielmo Feltrin.
其他題名:	a topological approach /
作者:	Feltrin, Guglielmo.
出版者:	Cham :Springer International Publishing :2018.
面頁冊數:	xxix, 304 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Boundary value problems.
電子資源:	https://doi.org/10.1007/978-3-319-94238-4
ISBN:	9783319942384$q(electronic bk.)

Positive solutions to indefinite problemsa topological approach /
Feltrin, Guglielmo.

Positive solutions to indefinite problemsa topological approach /[electronic resource] :by Guglielmo Feltrin. - Cham :Springer International Publishing :2018. - xxix, 304 p. :ill., digital ;24 cm. - Frontiers in mathematics,1660-8046. - Frontiers in mathematics..

Introduction -- Part I - Superlinear indefinite problems -- Dirichlet boundary conditions -- More general nonlinearities f(t; s) -- Neumann and periodic conditions: existence results -- Neumann and periodic conditions: multiplicity results -- Subharmonic solutions and symbolic dynamics -- Part II - Super-sublinear indefinite problems -- Existence results -- High multiplicity results -- Subharmonic solutions and symbolic dynamics -- Part III - Appendices -- Leray-Schauder degree for locally compact operators -- Mawhin's coincidence degree -- Maximum principles and a change of variable -- Bibliography.

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.

ISBN: 9783319942384$q(electronic bk.)

Standard No.: 10.1007/978-3-319-94238-4doiSubjects--Topical Terms:

206979
Boundary value problems.

LC Class. No.: QA379 / .F458 2018

Dewey Class. No.: 515.35

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505 0 $a Introduction -- Part I - Superlinear indefinite problems -- Dirichlet boundary conditions -- More general nonlinearities f(t; s) -- Neumann and periodic conditions: existence results -- Neumann and periodic conditions: multiplicity results -- Subharmonic solutions and symbolic dynamics -- Part II - Super-sublinear indefinite problems -- Existence results -- High multiplicity results -- Subharmonic solutions and symbolic dynamics -- Part III - Appendices -- Leray-Schauder degree for locally compact operators -- Mawhin's coincidence degree -- Maximum principles and a change of variable -- Bibliography.
520 $a 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.
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