LEADER 04628nam 22007695 450 001 9910300259603321 005 20221118235257.0 010 $a3-319-25289-5 024 7 $a10.1007/978-3-319-25289-6 035 $a(CKB)3710000000521715 035 $a(EBL)4107659 035 $a(SSID)ssj0001585638 035 $a(PQKBManifestationID)16263757 035 $a(PQKBTitleCode)TC0001585638 035 $a(PQKBWorkID)14864167 035 $a(PQKB)10402546 035 $a(DE-He213)978-3-319-25289-6 035 $a(MiAaPQ)EBC4107659 035 $a(PPN)190523476 035 $a(EXLCZ)993710000000521715 100 $a20151124d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 12$aA variational approach to Lyapunov type inequalities $efrom ODEs to PDEs /$fby Antonio Cañada, Salvador Villegas 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (136 p.) 225 1 $aSpringerBriefs in Mathematics,$x2191-8198 300 $aDescription based upon print version of record. 311 $a3-319-25287-9 320 $aIncludes bibliographical references at the end of each chapters and index. 327 $a1. Introduction -- 2. A variational characterization of the best Lyapunov constants -- 3. Higher eigenvalues -- 4. Partial differential equations -- 5. Systems of equations -- Index. 330 $aThis book highlights the current state of Lyapunov-type inequalities through a detailed analysis. Aimed toward researchers and students working in differential equations and those interested in the applications of stability theory and resonant systems, the book begins with an overview Lyapunov?s original results and moves forward to include prevalent results obtained in the past ten years. Detailed proofs and an emphasis on basic ideas are provided for different boundary conditions for ordinary differential equations, including Neumann, Dirichlet, periodic, and antiperiodic conditions. Novel results of higher eigenvalues, systems of equations, partial differential equations as well as variational approaches are presented. To this respect, a new and unified variational point of view  is introduced for the treatment of such problems and a systematic discussion of different types of boundary conditions is featured. Various problems make the study of Lyapunov-type inequalities of interest to those in pure and applied mathematics. Originating with the study of the stability properties of the Hill equation, other questions arose for instance in systems at resonance, crystallography, isoperimetric problems, Rayleigh type quotients and oscillation and intervals of disconjugacy and it lead to the study of Lyapunov-type inequalities for differential equations. This classical area of mathematics is still of great interest and remains a source of inspiration.  . 410 0$aSpringerBriefs in Mathematics,$x2191-8198 606 $aDifferential equations 606 $aDifferential equations, Partial 606 $aDifference equations 606 $aFunctional equations 606 $aIntegral transforms 606 $aCalculus, Operational 606 $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aDifference and Functional Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12031 606 $aIntegral Transforms, Operational Calculus$3https://scigraph.springernature.com/ontologies/product-market-codes/M12112 615 0$aDifferential equations. 615 0$aDifferential equations, Partial. 615 0$aDifference equations. 615 0$aFunctional equations. 615 0$aIntegral transforms. 615 0$aCalculus, Operational. 615 14$aOrdinary Differential Equations. 615 24$aPartial Differential Equations. 615 24$aDifference and Functional Equations. 615 24$aIntegral Transforms, Operational Calculus. 676 $a515.354 700 $aCañada$b Antonio$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755680 702 $aVillegas$b Salvador$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300259603321 996 $aA Variational Approach to Lyapunov Type Inequalities$92544811 997 $aUNINA