The Resource Lyapunovtype inequalities : with applications to Eigenvalue problems, Juan Pablo Pinasco, (electronic book)
Lyapunovtype inequalities : with applications to Eigenvalue problems, Juan Pablo Pinasco, (electronic book)
Resource Information
The item Lyapunovtype inequalities : with applications to Eigenvalue problems, Juan Pablo Pinasco, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.This item is available to borrow from 1 library branch.
Resource Information
The item Lyapunovtype inequalities : with applications to Eigenvalue problems, Juan Pablo Pinasco, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.
This item is available to borrow from 1 library branch.
 Summary
 The eigenvalue problems for quasilinear and nonlinear operators present many differences with the linear case, and a Lyapunov inequality for quasilinear resonant systems showed the existence of eigenvalue asymptotics driven by the coupling of the equations instead of the order of the equations. For p=2, the coupling and the order of the equations are the same, so this cannot happen in linear problems. Another striking difference between linear and quasilinear second order differential operators is the existence of Lyapunovtype inequalities in Rn when p>n. Since the linear case corresponds to p=2, for the usual Laplacian there exists a Lyapunov inequality only for onedimensional problems. For linear higher order problems, several Lyapunovtype inequalities were found by Egorov and Kondratiev and collected in On spectral theory of elliptic operators, Birkhauser Basel 1996. However, there exists an interesting interplay between the dimension of the underlying space, the order of the differential operator, the Sobolev space where the operator is defined, and the norm of the weight appearing in the inequality which is not fully developed. Also, the Lyapunov inequality for differential equations in Orlicz spaces can be used to develop an oscillation theory, bypassing the classical sturmian theory which is not known yet for those equations. For more general operators, like the p(x) laplacian, the possibility of existence of Lyapunovtype inequalities remains unexplored
 Language
 eng
 Extent
 1 online resource (xiii, 131 pages.)
 Isbn
 9781461485223
 Label
 Lyapunovtype inequalities : with applications to Eigenvalue problems
 Title
 Lyapunovtype inequalities
 Title remainder
 with applications to Eigenvalue problems
 Statement of responsibility
 Juan Pablo Pinasco
 Language
 eng
 Summary
 The eigenvalue problems for quasilinear and nonlinear operators present many differences with the linear case, and a Lyapunov inequality for quasilinear resonant systems showed the existence of eigenvalue asymptotics driven by the coupling of the equations instead of the order of the equations. For p=2, the coupling and the order of the equations are the same, so this cannot happen in linear problems. Another striking difference between linear and quasilinear second order differential operators is the existence of Lyapunovtype inequalities in Rn when p>n. Since the linear case corresponds to p=2, for the usual Laplacian there exists a Lyapunov inequality only for onedimensional problems. For linear higher order problems, several Lyapunovtype inequalities were found by Egorov and Kondratiev and collected in On spectral theory of elliptic operators, Birkhauser Basel 1996. However, there exists an interesting interplay between the dimension of the underlying space, the order of the differential operator, the Sobolev space where the operator is defined, and the norm of the weight appearing in the inequality which is not fully developed. Also, the Lyapunov inequality for differential equations in Orlicz spaces can be used to develop an oscillation theory, bypassing the classical sturmian theory which is not known yet for those equations. For more general operators, like the p(x) laplacian, the possibility of existence of Lyapunovtype inequalities remains unexplored
 Cataloging source
 GW5XE
 http://library.link/vocab/creatorName
 Pinasco, Juan Pablo
 Dewey number
 515.352
 Index
 no index present
 LC call number
 QA871
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Series statement
 SpringerBriefs in Mathematics,
 http://library.link/vocab/subjectName
 Lyapunov functions
 Label
 Lyapunovtype inequalities : with applications to Eigenvalue problems, Juan Pablo Pinasco, (electronic book)
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references
 Color
 multicolored
 Control code
 SPR859400654
 Dimensions
 unknown
 Extent
 1 online resource (xiii, 131 pages.)
 File format
 unknown
 Form of item
 online
 Isbn
 9781461485223
 Level of compression
 unknown
 Other control number
 10.1007/9781461485230
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Reproduction note
 Electronic resource.
 Sound
 unknown sound
 Specific material designation
 remote
 Label
 Lyapunovtype inequalities : with applications to Eigenvalue problems, Juan Pablo Pinasco, (electronic book)
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references
 Color
 multicolored
 Control code
 SPR859400654
 Dimensions
 unknown
 Extent
 1 online resource (xiii, 131 pages.)
 File format
 unknown
 Form of item
 online
 Isbn
 9781461485223
 Level of compression
 unknown
 Other control number
 10.1007/9781461485230
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Reproduction note
 Electronic resource.
 Sound
 unknown sound
 Specific material designation
 remote
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.liverpool.ac.uk/portal/Lyapunovtypeinequalitieswithapplicationsto/XF8IT1SfdQ/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.liverpool.ac.uk/portal/Lyapunovtypeinequalitieswithapplicationsto/XF8IT1SfdQ/">Lyapunovtype inequalities : with applications to Eigenvalue problems, Juan Pablo Pinasco, (electronic book)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.liverpool.ac.uk/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.liverpool.ac.uk/">University of Liverpool</a></span></span></span></span></div>