LEADER 04532nam 2200709 450 001 9910462706403321 005 20211216210755.0 010 $a3-11-029531-8 024 7 $a10.1515/9783110295313 035 $a(CKB)2670000000432722 035 $a(EBL)1130300 035 $a(OCoLC)858762153 035 $a(SSID)ssj0001001979 035 $a(PQKBManifestationID)11569904 035 $a(PQKBTitleCode)TC0001001979 035 $a(PQKBWorkID)10995749 035 $a(PQKB)11087752 035 $a(MiAaPQ)EBC1130300 035 $a(DE-B1597)178526 035 $a(OCoLC)880737219 035 $a(OCoLC)900720890 035 $a(DE-B1597)9783110295313 035 $a(Au-PeEL)EBL1130300 035 $a(CaPaEBR)ebr10786205 035 $a(CaONFJC)MIL807887 035 $a(EXLCZ)992670000000432722 100 $a20130930h20132013 uy 0 101 0 $aeng 135 $aurnn#---|u||u 181 $ctxt 182 $cc 183 $acr 200 10$aImpulsive differential inclusions $ea fixed point approach /$fby John R. Graef, Johnny Henderson, Abdelghani Ouahab 210 1$aBerlin ;$aBoston :$cWalter de Gruyter GmbH & Co., KG,$d[2013] 210 4$dİ2013 215 $a1 online resource (412 p.) 225 0 $aDe Gruyter Series in Nonlinear Analysis and Applications ;$v20 300 $aDescription based upon print version of record. 311 0 $a3-11-029361-7 327 $tFront matter --$tContents --$tNotations --$tChapter 1. Introduction and Motivations --$tChapter 2. Preliminaries --$tChapter 3. FDEs with Infinite Delay --$tChapter 4. Boundary Value Problems on Infinite Intervals --$tChapter 5. Differential Inclusions --$tChapter 6. Differential Inclusions with Infinite Delay --$tChapter 7. Impulsive FDEs with Variable Times --$tChapter 8. Neutral Differential Inclusions --$tChapter 9. Topology and Geometry of Solution Sets --$tChapter 10. Impulsive Semilinear Differential Inclusions --$tChapter 11. Selected Topics --$tAppendix --$tBibliography --$tIndex 330 $aDifferential equations with impulses arise as models of many evolving processes that are subject to abrupt changes, such as shocks, harvesting, and natural disasters. These phenomena involve short-term perturbations from continuous and smooth dynamics, whose duration is negligible in comparison with the duration of an entire evolution. In models involving such perturbations, it is natural to assume these perturbations act instantaneously or in the form of impulses. As a consequence, impulsive differential equations have been developed in modeling impulsive problems in physics, population dynamics, ecology, biotechnology, industrial robotics, pharmacokinetics, optimal control, and so forth. There are also many different studies in biology and medicine for which impulsive differential equations provide good models. During the last 10 years, the authors have been responsible for extensive contributions to the literature on impulsive differential inclusions via fixed point methods. This book is motivated by that research as the authors endeavor to bring under one cover much of those results along with results by other researchers either affecting or affected by the authors' work. The questions of existence and stability of solutions for different classes of initial value problems for impulsive differential equations and inclusions with fixed and variable moments are considered in detail. Attention is also given to boundary value problems. In addition, since differential equations can be viewed as special cases of differential inclusions, significant attention is also given to relative questions concerning differential equations. This monograph addresses a variety of side issues that arise from its simpler beginnings as well. 410 3$aDe Gruyter Series in Nonlinear Analysis and Applications 606 $aBoundary value problems 606 $aDifferential equations 606 $aPrediction theory 606 $aStochastic processes 608 $aElectronic books. 615 0$aBoundary value problems. 615 0$aDifferential equations. 615 0$aPrediction theory. 615 0$aStochastic processes. 676 $a515/.352 700 $aGraef$b John R.$f1942-$042050 701 $aHenderson$b Johnny$0940289 701 $aOuahab$b Abdelghani$01027378 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910462706403321 996 $aImpulsive differential inclusions$92442778 997 $aUNINA