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Coincidence degree and periodic solutions of neutral equations. (English) Zbl 0274.34070

MSC:
34C25Periodic solutions of ODE
34K99Functional-differential equations
34A25Analytical theory of ODE (series, transformations, transforms, operational calculus, etc.)
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References:
[1] Hale, J. K.: Functional differential equations. Analytic theory of differential equations, 9-22 (1971) · Zbl 0222.34003
[2] Hale, J. K.: Oscillations in neutral functional differential equations. Nonlinear mechanics (1973) · Zbl 0267.34064
[3] Mawhin, J.: Equivalence theorems for nonlinear operator equations and coinci-dence degree theory for some mappings in locally convex topological vector spaces. J. differential equations 12, 610-636 (1972) · Zbl 0244.47049
[4] J. Mawhin, The solvability of some operator equations with a quasibounded nonlinearity in normed spaces, J. Math. Anal. Appl., to appear. · Zbl 0307.47060
[5] Mawhin, J.: Periodic solutions of nonlinear functional differential equations. J. differential equations 10, 240-261 (1971) · Zbl 0223.34055
[6] Cronin, J.: Periodic solutions of nonautonomous equations. Boll. univ. Mat. ital. (4) 6, 45-54 (1972) · Zbl 0269.34062
[7] Fennell, R. E.: Periodic solutions of functional differential equations. J. math. Anal. appl 39, 198-201 (1972) · Zbl 0243.34126
[8] J. Mawhin, Periodic solutions of some vector retarded functional differential equations, J. Math. Anal. Appl., to appear. · Zbl 0275.34070
[9] Sadovskii, B. N.: Soviet math. Dokl. 12, 1543-1547 (1971)
[10] Cruz, M. A.; Hale, J. K.: Stability of functional differential equations of neutral type. J. differential equations 7, 334-355 (1970) · Zbl 0191.38901
[11] Kato, T.: Perturbation theory for linear operators. (1966) · Zbl 0148.12601
[12] Ghanas, A.: The theory of compact vector fields and some of its applications to topology of functional spaces (I). Rozpravy mat. Přírod věd. \V{c}eskoslovenské akad. Věd. r\breve{}ada 30, 1-93 (1962)
[13] Miranker, W.: Periodic solutions of the wave equation with a nonlinear interface condition. IBM J. Res. develop 5, 2-24 (1961) · Zbl 0148.08405
[14] Lopes, O.: Asymptotic fixed point theorems and forced oscillations in neutral equations. Ph.d. thesis (June 1973)