Weakly continuous nonlinear accretive operators in reflexive Banach spaces
Author:
W. E. Fitzgibbon
Journal:
Proc. Amer. Math. Soc. 41 (1973), 229236
MSC:
Primary 47H15; Secondary 34G05
MathSciNet review:
0324496
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Abstract: Let be a reflexive space and be a weakly continuous (possibly nonlinear) operator which maps to . We are concerned with the autonomous differential equation We first provide a local solution to (1.1) and then we apply the additional hypothesis that is accretive to extend the local solution of (1.1) to a global solution. If is weakly continuous and accretive then is shown to be accretive, i.e. for all . The accretiveness of enables us to provide a semigroup representation of solutions to (1.1), We then investigate properties of semigroups which have weakly continuous infinitesimal generators.
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 S. Chow and J. D. Schuur, An existence theorem for ordinary differential equations in Banach spaces, Bull. Amer. Math. Soc. 77 (1971), 10181020. MR 44 #4334. MR 0287127 (44:4334)
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 C. Yen, The convergence, periodicity and rest point behaviour of orbits in nonlinear semigroups of contractions, Pacific J. Math. (to appear).
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939197303244962
PII:
S 00029939(1973)03244962
Keywords:
Accretive,
weakly continuous,
semigroup of nonexpansive nonlinear operators
Article copyright:
© Copyright 1973 American Mathematical Society
