國立高雄大學圖資館 |

Language: English

Back

Positive solutions to indefinite pro...

Feltrin, Guglielmo.

Positive solutions to indefinite problemsa topological approach /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Positive solutions to indefinite problemsby Guglielmo Feltrin.
Reminder of title:	a topological approach /
Author:	Feltrin, Guglielmo.
Published:	Cham :Springer International Publishing :2018.
Description:	xxix, 304 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Boundary value problems.
Online resource:	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

Positive solutions to indefinite problemsa topological approach /
LDR:02818nmm a2200337 a 4500 001 547354
003 DE-He213
005 20190503104659.0
006 m d
007 cr nn 008maaau
008 190709s2018 gw s 0 eng d
020 $a 9783319942384$q(electronic bk.)
020 $a 9783319942377$q(paper)
024 7 $a 10.1007/978-3-319-94238-4 $2 doi
035 $a 978-3-319-94238-4
040 $a GP $c GP
041 0 $a eng
050 4 $a QA379 $b .F458 2018
072 7 $a PBKJ $2 bicssc
072 7 $a MAT007000 $2 bisacsh
072 7 $a PBKJ $2 thema
082 0 4 $a 515.35 $2 23
090 $a QA379 $b .F328 2018
100 1 $a Feltrin, Guglielmo. $3 826605
245 1 0 $a Positive solutions to indefinite problems $h [electronic resource] : $b a topological approach / $c by Guglielmo Feltrin.
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhauser, $c 2018.
300 $a xxix, 304 p. : $b ill., digital ; $c 24 cm.
490 1 $a Frontiers in mathematics, $x 1660-8046
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.
650 0 $a Boundary value problems. $3 206979
650 1 4 $a Ordinary Differential Equations. $3 273778
650 2 4 $a Operator Theory. $3 274795
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a Frontiers in mathematics. $3 558254
856 4 0 $u https://doi.org/10.1007/978-3-319-94238-4
950 $a Mathematics and Statistics (Springer-11649)