LEADER 04508nam 2200673 450 001 9910796663403321 005 20230808202716.0 010 $a3-11-038735-2 010 $a3-11-037844-2 024 7 $a10.1515/9783110378443 035 $a(CKB)3850000000001072 035 $a(EBL)4714784 035 $a(MiAaPQ)EBC4714784 035 $a(DE-B1597)429945 035 $a(OCoLC)959988756 035 $a(OCoLC)960759620 035 $a(DE-B1597)9783110378443 035 $a(Au-PeEL)EBL4714784 035 $a(CaPaEBR)ebr11279837 035 $a(CaONFJC)MIL961930 035 $a(EXLCZ)993850000000001072 100 $a20161227h20162016 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 10$aGeneralized inverse operators $eand Fredholm boundary-value problems /$fAlexander A. Boichuk, Anatolii M. Samoilenko 205 $a2nd ed. 210 1$aBerlin, [Germany] ;$aBoston, [Massachusetts] :$cDe Gruyter,$d2016. 210 4$dİ2016 215 $a1 online resource (314 p.) 225 1 $aInverse and Ill-Posed Problems Series,$x1381-4524 ;$vVolume 59 300 $aDescription based upon print version of record. 311 $a3-11-037845-0 311 $a3-11-037839-6 320 $aIncludes bibliographical references. 327 $tFrontmatter -- $tContents -- $tPreface -- $tPreface to the second edition -- $tNotation -- $tChapter 1. Preliminary Information -- $tChapter 2. Generalized Inverse Operators in Banach Spaces -- $tChapter 3. Pseudoinverse Operators in Hilbert Spaces -- $tChapter 4. Boundary-Value Problems for Operator Equations -- $tChapter 5. Boundary-Value Problems for Systems of Ordinary Differential Equations -- $tChapter 6. Impulsive Boundary-Value Problems for Systems of Ordinary Differential Equations -- $tChapter 7. Solutions of Differential and Difference Systems Bounded on the Entire Real Axis -- $tEpilogue -- $tBibliography -- $tBackmatter 330 $aThe book is devoted to the foundations of the theory of boundary-value problems for various classes of systems of differential-operator equations whose linear part is represented by Fredholm operators of the general form. A common point of view on numerous classes of problems that were traditionally studied independently of each other enables us to study, in a natural way, the theory of these problems, to supplement and improve the existing results, and in certain cases, study some of these problems for the first time.With the help of the technique of generalized inverse operators, the Vishik- Lyusternik method, and iterative methods, we perform a detailed investigation of the problems of existence, bifurcations, and branching of the solutions of linear and nonlinear boundary-value problems for various classes of differential-operator systems and propose new procedures for their construction.For more than 11 years that have passed since the appearance of the first edition of the monograph, numerous new publications of the authors in this direction have appeared. In this connection, it became necessary to make some additions and corrections to the previous extensively cited edition, which is still of signifi cant interest for the researchers.For researchers, teachers, post-graduate students, and students of physical and mathematical departments of universities. Contents:Preliminary InformationGeneralized Inverse Operators in Banach SpacesPseudoinverse Operators in Hilbert SpacesBoundary-Value Problems for Operator EquationsBoundary-Value Problems for Systems of Ordinary Differential EquationsImpulsive Boundary-Value Problems for Systems of Ordinary Differential EquationsSolutions of Differential and Difference Systems Bounded on the Entire Real Axis 410 0$aInverse and ill-posed problems series ;$vVolume 59. 606 $aFredholm equations 606 $aBoundary value problems 606 $aBanach spaces 606 $aOperator theory 615 0$aFredholm equations. 615 0$aBoundary value problems. 615 0$aBanach spaces. 615 0$aOperator theory. 676 $a515/.35 686 $aSK 620$qSEPA$2rvk 700 $aBoi?chuk$b A. A$g(Aleksandr Andreevich),$01499318 702 $aSamoi?lenko$b A. M$g(Anatolii? Mikhai?lovich), 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910796663403321 996 $aGeneralized inverse operators$93725247 997 $aUNINA