大葉大學圖書館 |

A variational approach to Lyapunov type inequalities[electronic resource] :from ODEs to PDEs /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
杜威分類號:	515.35
書名/作者:	A variational approach to Lyapunov type inequalities : from ODEs to PDEs // by Antonio Canada, Salvador Villegas.
作者:	Canada, Antonio.
其他作者:	Villegas, Salvador.
出版者:	Cham : : Springer International Publishing :, 2015.
面頁冊數:	xviii, 120 p. : : ill., digital ;; 24 cm.
Contained By:	Springer eBooks
標題:	Differential equations, Linear.
標題:	Differential equations, Partial.
標題:	Lyapunov stability.
標題:	Mathematics.
標題:	Ordinary Differential Equations.
標題:	Partial Differential Equations.
標題:	Difference and Functional Equations.
標題:	Integral Transforms, Operational Calculus.
ISBN:	9783319252896
ISBN:	9783319252872
內容註:	1. Introduction -- 2. A variational characterization of the best Lyapunov constants -- 3. Higher eigenvalues -- 4. Partial differential equations -- 5. Systems of equations -- Index.
摘要、提要註:	This book highlights the current state of Lyapunov-type inequalities through a detailed analysis. Aimed toward researchers and students working in differential equations and those interested in the applications of stability theory and resonant systems, the book begins with an overview Lyapunov's original results and moves forward to include prevalent results obtained in the past ten years. Detailed proofs and an emphasis on basic ideas are provided for different boundary conditions for ordinary differential equations, including Neumann, Dirichlet, periodic, and antiperiodic conditions. Novel results of higher eigenvalues, systems of equations, partial differential equations as well as variational approaches are presented. To this respect, a new and unified variational point of view is introduced for the treatment of such problems and a systematic discussion of different types of boundary conditions is featured. Various problems make the study of Lyapunov-type inequalities of interest to those in pure and applied mathematics. Originating with the study of the stability properties of the Hill equation, other questions arose for instance in systems at resonance, crystallography, isoperimetric problems, Rayleigh type quotients and oscillation and intervals of disconjugacy and it lead to the study of Lyapunov-type inequalities for differential equations. This classical area of mathematics is still of great interest and remains a source of inspiration.
電子資源:	http://dx.doi.org/10.1007/978-3-319-25289-6

A variational approach to Lyapunov type inequalities[electronic resource] :from ODEs to PDEs /
Canada, Antonio.

A variational approach to Lyapunov type inequalitiesfrom ODEs to PDEs /[electronic resource] :by Antonio Canada, Salvador Villegas. - Cham :Springer International Publishing :2015. - xviii, 120 p. :ill., digital ;24 cm. - SpringerBriefs in mathematics,2191-8198. - SpringerBriefs in mathematics..

1. Introduction -- 2. A variational characterization of the best Lyapunov constants -- 3. Higher eigenvalues -- 4. Partial differential equations -- 5. Systems of equations -- Index.

This book highlights the current state of Lyapunov-type inequalities through a detailed analysis. Aimed toward researchers and students working in differential equations and those interested in the applications of stability theory and resonant systems, the book begins with an overview Lyapunov's original results and moves forward to include prevalent results obtained in the past ten years. Detailed proofs and an emphasis on basic ideas are provided for different boundary conditions for ordinary differential equations, including Neumann, Dirichlet, periodic, and antiperiodic conditions. Novel results of higher eigenvalues, systems of equations, partial differential equations as well as variational approaches are presented. To this respect, a new and unified variational point of view is introduced for the treatment of such problems and a systematic discussion of different types of boundary conditions is featured. Various problems make the study of Lyapunov-type inequalities of interest to those in pure and applied mathematics. Originating with the study of the stability properties of the Hill equation, other questions arose for instance in systems at resonance, crystallography, isoperimetric problems, Rayleigh type quotients and oscillation and intervals of disconjugacy and it lead to the study of Lyapunov-type inequalities for differential equations. This classical area of mathematics is still of great interest and remains a source of inspiration.

ISBN: 9783319252896

Standard No.: 10.1007/978-3-319-25289-6doiSubjects--Topical Terms:

469164
Differential equations, Linear.

LC Class. No.: QA372

Dewey Class. No.: 515.35

A variational approach to Lyapunov type inequalities[electronic resource] :from ODEs to PDEs /
LDR:02683nam a2200325 a 4500 001 444312
003 DE-He213
005 20160415163807.0
006 m d
007 cr nn 008maaau
008 160715s2015 gw s 0 eng d
020 $a 9783319252896 $q (electronic bk.)
020 $a 9783319252872 $q (paper)
024 7 $a 10.1007/978-3-319-25289-6 $2 doi
035 $a 978-3-319-25289-6
040 $a GP $c GP
041 0 $a eng
050 4 $a QA372
072 7 $a PBKJ $2 bicssc
072 7 $a MAT007000 $2 bisacsh
082 0 4 $a 515.35 $2 23
090 $a QA372 $b .C212 2015
100 1 $a Canada, Antonio. $3 635751
245 1 2 $a A variational approach to Lyapunov type inequalities $h [electronic resource] : $b from ODEs to PDEs / $c by Antonio Canada, Salvador Villegas.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a xviii, 120 p. : $b ill., digital ; $c 24 cm.
490 1 $a SpringerBriefs in mathematics, $x 2191-8198
505 0 $a 1. Introduction -- 2. A variational characterization of the best Lyapunov constants -- 3. Higher eigenvalues -- 4. Partial differential equations -- 5. Systems of equations -- Index.
520 $a This book highlights the current state of Lyapunov-type inequalities through a detailed analysis. Aimed toward researchers and students working in differential equations and those interested in the applications of stability theory and resonant systems, the book begins with an overview Lyapunov's original results and moves forward to include prevalent results obtained in the past ten years. Detailed proofs and an emphasis on basic ideas are provided for different boundary conditions for ordinary differential equations, including Neumann, Dirichlet, periodic, and antiperiodic conditions. Novel results of higher eigenvalues, systems of equations, partial differential equations as well as variational approaches are presented. To this respect, a new and unified variational point of view is introduced for the treatment of such problems and a systematic discussion of different types of boundary conditions is featured. Various problems make the study of Lyapunov-type inequalities of interest to those in pure and applied mathematics. Originating with the study of the stability properties of the Hill equation, other questions arose for instance in systems at resonance, crystallography, isoperimetric problems, Rayleigh type quotients and oscillation and intervals of disconjugacy and it lead to the study of Lyapunov-type inequalities for differential equations. This classical area of mathematics is still of great interest and remains a source of inspiration.
650 0 $a Differential equations, Linear. $3 469164
650 0 $a Differential equations, Partial. $3 389324
650 0 $a Lyapunov stability. $3 633580
650 1 4 $a Mathematics. $3 172349
650 2 4 $a Ordinary Differential Equations. $3 465742
650 2 4 $a Partial Differential Equations. $3 464931
650 2 4 $a Difference and Functional Equations. $3 464113
650 2 4 $a Integral Transforms, Operational Calculus. $3 602459
700 1 $a Villegas, Salvador. $3 635752
710 2 $a SpringerLink (Online service) $3 463450
773 0 $t Springer eBooks
830 0 $a SpringerBriefs in mathematics. $3 465744
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-25289-6
950 $a Mathematics and Statistics (Springer-11649)