LEADER 03504nam 2200589 450 001 9910484578503321 005 20230829233305.0 010 $a3-540-74775-3 024 7 $a10.1007/978-3-540-74775-8 035 $a(CKB)1000000000437246 035 $a(SSID)ssj0000320177 035 $a(PQKBManifestationID)11279040 035 $a(PQKBTitleCode)TC0000320177 035 $a(PQKBWorkID)10348250 035 $a(PQKB)10472971 035 $a(DE-He213)978-3-540-74775-8 035 $a(MiAaPQ)EBC3062877 035 $a(MiAaPQ)EBC6351797 035 $a(PPN)123735912 035 $a(EXLCZ)991000000000437246 100 $a20210217d2008 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aStability of nonautonomous differential equations /$fLuis Barreira, Claudia Valls 205 $a1st ed. 2008. 210 1$aBerlin, Germany ;$aNew York, New York :$cSpringer,$d[2008] 210 4$dİ2008 215 $a1 online resource (XIV, 291 p.) 225 0 $aLecture notes in mathematics ;$v1926 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-74774-5 320 $aIncludes bibliographical references (pages [277]-281) and index. 327 $aExponential dichotomies -- Exponential dichotomies and basic properties -- Robustness of nonuniform exponential dichotomies -- Stable manifolds and topological conjugacies -- Lipschitz stable manifolds -- Smooth stable manifolds in Rn -- Smooth stable manifolds in Banach spaces -- A nonautonomous Grobman?Hartman theorem -- Center manifolds, symmetry and reversibility -- Center manifolds in Banach spaces -- Reversibility and equivariance in center manifolds -- Lyapunov regularity and stability theory -- Lyapunov regularity and exponential dichotomies -- Lyapunov regularity in Hilbert spaces -- Stability of nonautonomous equations in Hilbert spaces. 330 $aMain theme of this volume is the stability of nonautonomous differential equations, with emphasis on the Lyapunov stability of solutions, the existence and smoothness of invariant manifolds, the construction and regularity of topological conjugacies, the study of center manifolds, as well as their reversibility and equivariance properties. Most results are obtained in the infinite-dimensional setting of Banach spaces. Furthermore, the linear variational equations are always assumed to possess a nonuniform exponential behavior, given either by the existence of a nonuniform exponential contraction or a nonuniform exponential dichotomy. The presentation is self-contained and has unified character. The volume contributes towards a rigorous mathematical foundation of the theory in the infinite-dimension setting, and may lead to further developments in the field. The exposition is directed to researchers as well as graduate students interested in differential equations and dynamical systems, particularly in stability theory. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1926 606 $aLyapunov stability 606 $aDifferential equations 615 0$aLyapunov stability. 615 0$aDifferential equations. 676 $a515.392 700 $aBarreira$b Lui?s$f1968-$00 702 $aValls$b Claudia$f1973- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910484578503321 996 $aStability of nonautonomous differential equations$92831252 997 $aUNINA