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References
V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff Int. Publ., Leyden (The Netherlands), 1975
F. Browder, Nonlinear Operators and Nonlinear Equations of Evolution in Banach Spaces, Proc. Symp. Pure Appl. Math.,18, Part 2, Providence, 1975
B.D. Calvert and A.G. Kartsatos, On the compactness of the nonlinear evolution operator in a Banach space, Bull. London Math. Soc.19 (1987), 551–558
I. Cioranescu, Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems, Kluwer Acad. Publ., Boston, 1990
M.G. Crandall and T. Liggett, Generation of semigroups of nonlinear transformations in general Banach spaces, Amer. J. Math.93 (1971), 265–298
M.G. Crandall and A. Pazy, Nonlinear evolution equations in Banach spaces, Israel J. Math.11 (1972), 57–94
L.C. Evans, Nonlinear evolution equations in an arbitrary Banach space, Israel J. Math.26 (1977), 1–42
S. Gutman, Compact perturbations ofm-accretive operators in general Banach spaces, SIAM J. Math. Anal.13 (1982), 789–800
S. Gutman, Evolutions governed bym-accretive plus compact operators, Nonl. Anal. TMA7 (1983), 707–715
A.G. Kartsatos, Recent results involving compact perturbations and compact resolvents of accretive operators in Banach spaces, Proceedings of the World Congress of Nonlinear Analysts, Tampa, Florida, 1992, Walter De Gruyter, New York, 1994 (to appear)
A.G. Kartsatos, On the compactness of the evolution operator generated by certain nonlinear ω-accretive operators in general Banach spaces, Proc. Amer. Math. Soc., to appear
A.G. Kartsatos and K. Shin, Solvability of functional evolutions via compactness methods in general Banach spaces, Nonl. Anal. TMA21 (1993), 517–535
T. Kato, Nonlinear semigroups and evolution equations. J. Math. Soc. Japan19 (1967), 508–520
Y. Kobayashi, Difference approximation of Cauchy problems for quasi-dissipative operators and generation of nonlinear semigroups, J. Math. Soc. Japan27 (1975), 641–663
V. Lakshmikantham and S. Leela, Nonlinear Differential Equations in Abstract Spaces, Pergamon Press, Oxford, 1981
N.H. Pavel, Compact semigroups, invariance and positivity in differential equations, Proc. Symp. Aspects of Positivity in Functional Analysis, Tübingen, 1985, pp. 105–113
N.H. Pavel, Nonlinear Evolution Operators and Semigroups, Lect. Notes Math.,1260, Springer-Verlag, Berlin, 1987
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983
N. Tanaka, Nonlinear nonautonomous differential equations, R.I.M.S. Kokyuroku,647 (1988), 36–56
I.I. Vrabie, Compactness Methods for Nonlinear Evolutions, Longman Sci. Tech., Essex, 1987
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Results from this paper were announced at the International Conference on Functional Differential Equations in Guangzhou, China, May 25–30, 1993
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Kartsatos, A.G. A compact evolution operator generated by a nonlinear time-dependentm-accretive operator in a Banach space. Math. Ann. 302, 473–487 (1995). https://doi.org/10.1007/BF01444503
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DOI: https://doi.org/10.1007/BF01444503