LEADER 04612nam 22005655 450 001 9910955000403321 005 20250731082149.0 010 $a1-4612-0601-4 024 7 $a10.1007/978-1-4612-0601-9 035 $a(CKB)2660000000022899 035 $a(SSID)ssj0001297978 035 $a(PQKBManifestationID)11761651 035 $a(PQKBTitleCode)TC0001297978 035 $a(PQKBWorkID)11229637 035 $a(PQKB)11215817 035 $a(DE-He213)978-1-4612-0601-9 035 $a(MiAaPQ)EBC3074521 035 $a(PPN)238007014 035 $a(EXLCZ)992660000000022899 100 $a20110731d1998 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aOrdinary Differential Equations /$fby Wolfgang Walter 205 $a1st ed. 1998. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d1998. 215 $a1 online resource (XI, 384 p.) 225 1 $aGraduate Texts in Mathematics,$x2197-5612 ;$v182 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a0-387-98459-3 311 08$a1-4612-6834-6 320 $aIncludes bibliographical references and index. 327 $aI. First Order Equations: Some Integrable Cases -- § 1. Explicit First Order Equations -- § 2. The Linear Differential Equation. Related Equations -- § 3. Differential Equations for Families of Curves. Exact Equations -- § 4. Implicit First Order Differential Equations -- II: Theory of First Order Differential Equations -- § 5. Tools from Functional Analysis -- § 6. An Existence and Uniqueness Theorem -- § 7. The Peano Existence Theorem -- § 8. Complex Differential Equations. Power Series Expansions -- § 9. Upper and Lower Solutions. Maximal and Minimal Integrals -- III: First Order Systems. Equations of Higher Order -- § 10. The Initial Value Problem for a System of First Order -- § 11. Initial Value Problems for Equations of Higher Order -- § 12. Continuous Dependence of Solutions -- § 13. Dependence of Solutions on Initial Values and Parameters -- IV: Linear Differential Equations -- § 14. Linear Systems -- § 15. Homogeneous Linear Systems -- § 16. Inhomogeneous Systems -- § 17. Systems with Constant Coefficients -- § 18. Matrix Functions. Inhomogeneous Systems -- § 19. Linear Differential Equations of Order n -- § 20. Linear Equations of Order nwith Constant Coefficients -- V: Complex Linear Systems -- § 21. Homogeneous Linear Systems in the Regular Case -- § 22. Isolated Singularities -- § 23. Weakly Singular Points. Equations of Fuchsian Type -- § 24. Series Expansion of Solutions -- § 25. Second Order Linear Equations -- VI: Boundary Value and Eigenvalue Problems -- § 26. Boundary Value Problems -- § 27. The Sturm?Liouville Eigenvalue Problem -- § 28. Compact Self-Adjoint Operators in Hilbert Space -- VII: Stability and Asymptotic Behavior -- § 29. Stability -- § 30. The Method of Lyapunov -- A. Topology -- B. Real Analysis -- C. C0111plex Analysis -- D. FunctionalAnalysis -- Solutions and Hints for Selected Exercises -- Literature -- Notation. 330 $aDevelops the theory of initial-, boundary-, and eigenvalue problems, real and complex linear systems, asymptotic behavior and stability. Using novel approaches to many subjects, the book emphasizes differential inequalities and treats more advanced topics such as Caratheodory theory, nonlinear boundary value problems and radially symmetric elliptic problems. New proofs are given which use concepts and methods from functional analysis. Applications from mechanics, physics, and biology are included, and exercises, which range from routine to demanding, are dispersed throughout the text. Solutions for selected exercises are included at the end of the book. All required material from functional analysis is developed in the book and is accessible to students with a sound knowledge of calculus and familiarity with notions from linear algebra. This text would be an excellent choice for a course for beginning graduate or advanced undergraduate students. 410 0$aGraduate Texts in Mathematics,$x2197-5612 ;$v182 606 $aMathematical analysis 606 $aAnalysis 615 0$aMathematical analysis. 615 14$aAnalysis. 676 $a515 700 $aWalter$b Wolfgang$4aut$4http://id.loc.gov/vocabulary/relators/aut$0441828 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910955000403321 996 $aGewöhnliche Differentialgleichungen. Eine Einführung$93008503 997 $aUNINA