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Nonlinear semigroups and differential equations in Banach spaces

Author: Viorel Barbu
Publisher: Bucureşti : Editura Academiei, 1976.
Edition/Format:   Print book : English : Rev. and enlView all editions and formats
Database:WorldCat
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This book is concerned with nonlinear semigroups of contractions in Banach spaces and their application to the existence theory for differential equa- tions associated with nonlinear dissipative  Read more...

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Additional Physical Format: Online version:
Barbu, Viorel.
Nonlinear semigroups and differential equations in Banach spaces.
Bucureşti : Editura Academiei, 1976
(OCoLC)610176116
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Viorel Barbu
ISBN: 9028602054 9789028602052
OCLC Number: 2663769
Notes: Translation of Semigrupuri de contraçtii neliniare în spaţii Banach.
Description: 352 pages ; 25 cm
Contents: I Preliminaries.- 1. Metric properties of normed spaces.- 1.1 Duality mappings.- 1.2 Strictly convex normed spaces.- 1.3 Uniformly convex Banach spaces.- 2. Vectorial functions defined on real intervals.- 2.1 Absolutely continuous vectorial functions.- 2.2 Vectorial distributions and Wk,p spaces.- 2.3 Sobolev spaces.- 3. Semigroups of continuous linear operators.- 3.1 Semigroups of class (C0). Hille-Yosida theorem.- 3.2 Analytic semigroups.- 3.3 Nonhomogeneous linear differential equations.- II Nonlinear Operators in Banach Spaces.- 1. Maximal monotone operators.- 1.1 Definitions and fundamental concepts.- 1.2 A general perturbation theorem.- 1.3 A nonlinear elliptic boundary problem.- 2. Subdifferential mappings.- 2.1 Lower semicontinuous convex functions.- 2.2 Subdifferentials of convex functions.- 2.3 Some examples of cyclically monotone operators.- 3. Dissipative sets in Banach spaces.- 3.1 Basic properties of dissipative sets.- 3.2 Perturbations of dissipative sets.- 3.3 Riccati equations in Hilbert spaces.- Bibliographical notes.- III Differential Equations in Banach Spaces.- 1. Semigroups of nonlinear contractions in Banach spaces.- 1.1 General properties of nonlinear semigroups.- 1.2 The exponential formula.- 1.3 Convergence theorems.- 1.4 Generation of nonlinear semigroups.- 2. Quasi-autonomous differential equations.- 2.1 Existence theorems.- 2.2 Periodic solutions.- 2.3 Examples.- 3. Differential equations associated with continuous dissipative operators.- 3.1 A general existence result.- 3.2 Continuous perturbations of m-dissipative operators.- 3.3 Semi-linear second-order elliptic equations in L1.- 4. Time-dependent nonlinear differential equations.- 4.1 Evolution equations associated with dissipative sets.- 4.2 Evolution equations associated with nonlinear monotone hemicon-tinuous operators.- Bibliographical notes.- IV Nonlinear Differential Equations in Hilbert Spaces.- 1. Nonlinear semigroups in Hilbert spaces.- 1.1 Nonlinear version of the Hille-Yosida theorem.- 1.2 Exponential formulae.- 1.3 Invariant sets with respect to nonlinear semigroups.- 2. Smoothing effect on initial data.- 2.1 The case in which A = ? ?.- 2.2 The case in which int D(A) ? ?.- 2.3 Applications.- 3. Variational evolution inequations.- 3.1 Unilateral conditions on u(t).- 3.2 Unilateral conditions on $$ \frac{<!-- -->{du}}{<!-- -->{dt}}(t) $$.- 3.3 A class of nonlinear variational inequations.- 3.4 Applications.- 4. Nonlinear Volterra equations with positive kernels in Hilbert spaces.- 4.1 Positive kernels.- 4.2 Equation (4.1) with A = ? ?.- 4.3 Equation (4.1) with A demicontinuous.- 4.4 A class of integro-differential equations.- 4.5 Further investigation of the preceding case.- Bibliographical notes.- V Second Order Nonlinear Differential Equations.- 1. Nonlinear differential equations of hyperbolic type.- 1.1 The equation $$ \frac{<!-- -->{<!-- -->{d^2}u}}{<!-- -->{d{t^2}}} + Au + M\left( {\frac{<!-- -->{du}}{<!-- -->{dt}}} \right) \mathrel\backepsilon f $$.- 1.2 Further investigation of the preceding case.- 1.3 Examples.- 1.4 Singular perturbations and hyperbolic variational inequations.- 1.5 Nonlinear wave equation.- 2. Boundary value problems for second order nonlinear differential equations.- 2.1 A class of two-point boundary value problems.- 2.2 Examples.- 2.3 A boundary value problem on half-axis.- 2.4 The square root of a nonlinear maximal monotone operator.- Bibliographical notes.
Other Titles: Semigrupuri de contraçtii neliniare în spaţii Banach.
Responsibility: Viorel Barbu.

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