References
Bogdanowicz, W. M.: On the existence of almost periodic solutions for systems of ordinary nonlinear differential equations in Banach spaces. Arch. Rat. Mech. Analysis13, 364–370 (1963).
—— On existence of asymptotically almost periodic and periodic solutions of nonlinear operational-differential equations. Notices A.M.S.11, 69 (1964).
—— Existence and uniqueness of asymptotically almost periodic and almost periodic solutions of nonlinear operational-differential equations. Notices A.M.S.11, 145 (1964).
—— Existence of periodic solutions of nonlinear operational-differential equations. Notices A.M.S.11, 146 (1964).
—— On the existence of periodic solutions of nonlinear partial differential equations. Notices A.M.S.11, 450 (1964).
—— On the existence of almost periodic and asymptotically almost periodic solutions for nonlinear partial differential equations. Notices A.M.S.11, 450 (1964).
——, andJ. Welch: On a linear operator connected with almost periodic solutions of linear differential equations in Hilbert spaces. Notices A.M.S.12, 55 (1965).
—— —— On a linear operator connected with almost periodic solutions of linear differential equations in Banach spaces. Notices A.M.S.12, 606 (1965).
Taam, C. T.: Stability, periodicity, and almost periodicity of solutions of nonlinear differential equations in Banach spaces. J. Math. Mechanics15, 849–876 (1966).
——, andJ. Welch: Compact solutions of nonlinear differential equations in Banach spaces. Michigan Math. J.13, 271–284 (1966).
Dunford, N., andJ. T. Schwartz: Linear operators I. New York: Interscience Publishers, Inc. 1958.
Weil, A.: Almost periodic invariant vector sets in metric vector spaces. Am. J. Math.71, 178–205 (1949).
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The research ofW. Bogdanowicz was supported by National Science Foundation Grant GP 2565, and the research ofJ. Welch was partly supported by the U. S. Army Research Office, Durham, under Contract DA-31-124-ARO-D-271.
The main results of this paper have been presented to the American Mathematical Society in [7] and [8].
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Bogdanowicz, W.M., Welch, J.N. On a linear operator connected with almost periodic solutions of linear differential equations in Banach spaces. Math. Ann. 172, 327–335 (1967). https://doi.org/10.1007/BF01351595
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DOI: https://doi.org/10.1007/BF01351595