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From Contents:
◊ Dissipative sets in Banach spaces
◊ Quasi-autonomous differential equations
◊ Nonlinear differential equations in Hilbert spaces
◊ Variational evolution inequations
◊ Nonlinear Volterra equations with positive kernels in Hilbert spaces
◊ Boundary value problems for second order nonlinear differential equations
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This is a reprinted edition of the book published in 1976 by the Noordhoff and Publishing House of the Romanian Academy. It is concerned with basic results of theory of nonlinear semigroups of contractions in Banach spaces and its applications to partial differential equations. This was the first monograph devoted to this subject and it still remains a reference book in the field being quoted so far in about 1500 research papers and monographs. The main topics treated here are the following: maximal monotone nonlinear operators in Banach spaces, m-accretive nonlinear operators, nonlinear semigroups of contractions and their infinitesimal generators, the Cauchy problem associated with nonlinear m-accretive (dissipative) operators in Banach spaces and applications to the existence theory of nonlinear parabolic and hyperbolic problems. Applications also include the treatment of nonlinear Volterra equations with complete monotone kernels and two points nonlinear boundary value problems.
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