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Invariant sets for perturbed semigroups of linear operators. (English) Zbl 0315.34074


MSC:

34G99 Differential equations in abstract spaces
45D05 Volterra integral equations
47J05 Equations involving nonlinear operators (general)
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References:

[1] Barbu, V., Continuous perturbations of nonlinear m-accretive operators in Banach spaces, Boll. Un. Mat. Italiana, 6, 270-278 (1972) · Zbl 0256.47053
[2] Butzer, P. L.; Berens, H., Semi-Groups of Operators and Approximation (1967), New York: Springer-Verlag, New York · Zbl 0164.43702
[3] H. Cartan,Calcul Differential, Paris, 1967. · Zbl 0156.36102
[4] Crandall, M. G.; Liggett, T., Generation of semi-groups of nonlinear transformations on general Banach spaces, Amer. J. Math., 113, 265-298 (1971) · Zbl 0226.47038
[5] D. L. Lovelady,A Hammerstein-Volterra integral equation with a linear semigroup convolution kernal, Indiana Univ. Math. J. (to appear). · Zbl 0278.45002
[6] Martin, R. H. Jr., Differential equations on closed subsets of a Banach space, Trans. Amer. Math. Soc., 179, 399-414 (1973) · Zbl 0293.34092 · doi:10.2307/1996511
[7] Martin, R. H. Jr., Approximation and existence of solutions to ordinary differential equations in Banach space, Funk. Ekvac., 16, 195-211 (1973) · Zbl 0296.34058
[8] Nagumo, M., Über die Laga der Integralkuruen gewohnlicher Differentialglerchugen, Proc. Phys.-Math. Soc. Japan, 24, 551-559 (1942) · Zbl 0061.17204
[9] N. Pavel,Approximate solutions of Cauchy problems for some differential equations on Banach spaces (to appear).
[10] Segal, I., Nonlinear semi-groups, Ann. of Math., 78, 339-364 (1963) · Zbl 0204.16004 · doi:10.2307/1970347
[11] Webb, G. F., Continuous nonlinear perturbations of linear accretive operators in Banach spaces, J. Funct. Anal., 10, 191-203 (1972) · Zbl 0245.47052 · doi:10.1016/0022-1236(72)90048-1
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