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Nichtlineare Gleichungen Und Abbildungsgrade by K. Deimling

Nichtlineare Gleichungen Und Abbildungsgrade

by K. Deimling
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Book cover type: Paperback
  • ISBN13: 9783540068884
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 134
  • Original Price: EUR 51.39
  • Language: German
  • Edition: N/A
  • Item Weight: 245 grams
  • BISAC Subject(s): Mathematical Analysis

Die mathematische Beschreibung naturwissenschaftlicher Vorgange fuhrt in den meisten Fallen auf Gleichungen der Form Fx = y, wobei die Ab- bildung F: X + Y und das Element ye Y gegeben sind, und eine Lasung x E X gesucht wird. Gelegentlich kommen auch Ungleichungen vor, worauf wir jedoch in dieser Vorlesung nicht eingehen. Wir haben gleich die Frage nach der Existenz von Lasungen gestellt, da wir hauptsachlich an einer positiven Antwort interessiert sind, obwohl es auch bemerkenswert viele Situationen gibt, in denen man das Gegenteil haben will. Wenn wir sicher sind, daB mindestens eine Lasung vorhanden ist, fragen wir wei- ter, ob es nur diese oder noch andere Losungen gibt. Auch diese Eindeu- tigkeitsfrage ist zwiespaltig. Oft ist die eindeutige Losbarkeit er- wunscht, oft sind aber gerade die Gleichungen besonders wichtig, die mehrere Lasungen haben; auBerdem ist zu unterscheiden zwischen lokaler Eindeutigkeit, die nur besagt, daB in einer gewissen Umgebung einer Lasung keine weiteren existieren, und globaler Eindeutigkeit, bei der es uberhaupt nur ein x e X mit Fx = y gibt. Will man beispielsweise eine nxn-Matrix A invertieren, so darfAx = 0 nur die Lasung x = 0 haben; andererseits geben gerade die Eigenwerte A von A, oder anders ausgedrlickt, die Gleichungen (A-AI)x = 0 mit meh- reren Lasungen, die beste Einsicht in das Verhalten der Abbildung A Belastet man einen vertikal eingespannten Stab, so muB selbst der auf Sicherheit Bedachte, d. h.

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