This is an elementary text - requiring a minimum of knowledge in the field - about very classical function analysis, combined with results of differential equations in Hilbert or Banach spaces. The author presents results from abstract Cauchy problems - in implicit or explicit form - and related semigroups of operators, weak and ultraweak solutions, the uniqueness of bounded ultra solutions. He also offers some results about almost-periodic solution, and an asymptotic result for a differential inequality in ultra-weak form.
Reihe
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Illustrationen
Maße
Höhe: 229 mm
Breite: 152 mm
ISBN-13
978-0-8493-0689-1 (9780849306891)
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Schweitzer Klassifikation
Hilbert space - definitions, first results; Banach spaces and linear operators; duality - the Hahn-Banach extension theorem; some singular (implicit) abstract differential equations; semigroups of class Co and the abstract Cauchy problem; compact linear operators; continuous symmetric operators in Hilbert spaces; semidynamical systems and Co semigroups; uniqueness of ultraweak solutions for a second order abstract Cauchy problem in Banach space; uniqueness of bounded ultraweak solutions in Hilbert space; almost periodic solutions (I); the well-posed ultraweak Cauchy problem and related semigroups of operators; asymptotic result for ultraweak differential inequalities in Hilbert space; almost periodic solutions (II); variational forms of the equation Au=f in Hilbert space; solution of the weak Neumann problem in an arbitrary open set of Rn.
