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Periodic solutions of nonlinear functional differential equations. (English) Zbl 0223.34055

MSC:
34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
34K05 General theory of functional-differential equations
34C25 Periodic solutions to ordinary differential equations
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[1] Halanay, A, Differential equations: stability, oscillations, time lags, (1966), Academic Press New York · Zbl 0144.08701
[2] Hale, J.K, Geometric theory of functional-differential equations, (), 247-266 · Zbl 0189.39904
[3] Perello, C, A note on periodic solutions of nonlinear differential equations with time lags, (), 185-187 · Zbl 0173.09801
[4] Mawhin, J, Equations intégrales et solutions périodiques des systèmes différentiels non linéaires, Bull. acad. R. belgique, cl. sci., 55, 934-947, (1969), (5) · Zbl 0193.06103
[5] Leray, J; Schauder, J, Topologie et équations fonctionnelles, Ann. ec. norm. sup., 51, 45-78, (1934), (3) · JFM 60.0322.02
[6] Cronin, J, Fixed points and topological degree in nonlinear analysis, (1964), American Mathematical Society Providence, R. I · Zbl 0117.34803
[7] Schwartz, J.T, Nonlinear functional analysis, New York university lecture notes, (1965), New York · Zbl 0203.14501
[8] Güssefeldt, G, Der topologische abbildungsgrad für vollstetige vektorfelder zum nachweis von periodische Lösungen, Math. nachr., 36, 231-233, (1968) · Zbl 0182.42102
[9] Reissig, R; Sansone, G; Conti, R, Nichtlineare differentialgleichungen höherer ordnung, (1969), Cremonese Roma · Zbl 0172.10801
[10] Mawhin, J, Degré topologique et solutions périodiques des systèmes différentiels non linéaires, Bull. soc. R. sci. liège, 38, 308-398, (1969) · Zbl 0186.41704
[11] Krasnosel’skii, M.A; Perov, A.I, On a existence principle for bounded, periodic and almost periodic solutions of systems of ordinary differential equations, Dokl. akad. nauk SSSR, 123, 235-238, (1958), (Russian) · Zbl 0088.06504
[12] Krasnosel’skii, M.A; Perov, A.I, Some criteria for existence of periodic solutions of systems of ordinary differential equations, (), 202-211, (Russian, Engl. Summ.)
[13] Krasnosel’skii, M.A, An alternative principle for establishing the existence of periodic solutions of differential equations with a lagging argument, Soviet math. dokl., 4, 1412-1415, (1963) · Zbl 0143.10603
[14] Krasnosel’skii, M.A; Strygin, V.V, Certain tests for the existence of periodic solutions for ordinary differential equations, Soviet math. dokl., 5, 763-766, (1964) · Zbl 0132.32102
[15] Strygin, V.V, On the dependence of an integral operator on a parameter, Soviet math. dokl., 5, 1433-1436, (1964) · Zbl 0143.31002
[16] Krasnosel’skii, M.A, The operator of translation along the trajectories of differential equations, (1968), American Mathematical Society Providence, R. I
[17] Krasnosel’skii, M.A, The theory of periodic solutions of non-autonomous differential equations, Russian math. surveys, 21, 53-74, (1966) · Zbl 0163.32701
[18] Cronin, J, Periodic solutions of some nonlinear differential equations, J. differential equations, 3, 31-46, (1967) · Zbl 0153.12401
[19] Mawhin, J, Periodic solutions of strongly nonlinear differential systems, (), to appear · Zbl 0243.34075
[20] Borisovich, Yu.G, The Poincaré-Andronov method in the problem of periodic solutions of differential equations with a lag, Soviet math. dokl., 4, 1388-1391, (1963) · Zbl 0151.10201
[21] Borisovich, Yu.G; Subbotin, V.F, The shift operator over trajectories of equations of evolution and periodic solutions, Soviet math. dokl., 8, 781-785, (1967) · Zbl 0173.09703
[22] Cooke, K.L, Forced periodic solutions of a stable non-linear differential-difference equation, Ann. of math., 61, 381-387, (1955) · Zbl 0066.33504
[23] Faure, R, Sur l’existence de certaines solutions périodiques et méthodes de Leray-Schauder: excitation paramétrique et équations différentielles aux différences, (), 261-266 · Zbl 0161.06602
[24] Hale, J.K, Periodic and almost periodic solutions of functional-differential equations, Arch. rational mech. anal., 15, 289-304, (1964) · Zbl 0129.06006
[25] Jones, G.S, Asymptotic fixed point theorems and periodic systems of functional-differential equations, Contr. diff. equ., 2, 385-405, (1963)
[26] Mitropolsky, Yu.A; Martiniuk, D.I, Lectures on the theory of oscillating systems with lags, (1969), Akad. Nauk. Ukr. SSR Kiev, (Russian)
[27] Yoshizawa, T, Ultimate boundedness of solutions and periodic solutions of functional-differential equations, (), 167-179 · Zbl 0173.35504
[28] Ziegler, H.J, Sur une note de M. C. perello sur des solutions périodiques d’équations fonctionnelles différentielles, C.R. acad. sci. Paris ser. A, 267, 783-785, (1968) · Zbl 0172.12304
[29] Cesari, L, Functional analysis and periodic solutions of non-linear differential equations, Contr. diff. equ., 1, 149-187, (1963)
[30] Hale, J.K, Ordinary differential equations, (1969), Interscience New York · Zbl 0186.40901
[31] Krasnosel’skii, M.A, Topological methods in the theory of nonlinear integral equations, (1963), Pergamon Oxford
[32] Zubov, V.I, Methods of A. M. Lyapunov and their application, (1964), Noordhoff Groningen · Zbl 0115.30204
[33] Lefschetz, S, The critical case in differential equations, Bol. soc. mat. mexicana, 6, 5-18, (1961), (2) · Zbl 0101.30401
[34] {\scJ. Mawhin}, Existence of periodic solutions for higher-order differential systems that are not of class D, J. Differential Equations, to appear. · Zbl 0224.34034
[35] {\scJ. Mawhin}, An extension of a theorem of A. C. Lazer on forced nonlinear oscillations, J. Math. Anal. Appl., to appear. · Zbl 0213.10804
[36] Graves, L.M, The theory of functions of real variables, (1946), McGraw-Hill New York · Zbl 0063.01720
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