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Periodic boundary value problems for third order differential equations. (English) Zbl 0753.34013
Summary: There are studied the questions of existence of periodic solutions of the equation
\(u'''=f(t,u,u',u'')\) by means of topological degree methods.

MSC:
34B15 Nonlinear boundary value problems for ordinary differential equations
46E15 Banach spaces of continuous, differentiable or analytic functions
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
34C25 Periodic solutions to ordinary differential equations
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References:
[1] BATES P. W., WARD Y. R.: Periodic solutions of higher order systems. Pacif. J. Math., 84 (1979), 275-282. · Zbl 0424.34042
[2] GAINES R. E., MAWHIN J. L.: Coincidence Degree and Nonlinear Differential Equations. Springer-Verlag, Berlin-Heidelberg-New York, 1977. · Zbl 0339.47031
[3] GEGELIA G. T.: On boundary problems of the periodic type for ordinary differential equations. (Russian). Trudy IPM, Tbilisi, 17 (1986), 60-93. · Zbl 0632.34010
[4] KIBENKO A. V., KIPNIS A. A.: On periodic solutions of nonlinear differential equations of the 3rd order. (Russian). Priklad. anal., Voronež, (1979), 70-72.
[5] KIGURADZE I. T., PŮŽA B.: On some boundary value problems for ordinary differential systems. (Russian). Diff. Ur., 12 (1976), 2139-2148.
[6] MAWHIN J. L.: Topological Degree Methods in Nonlinear Boundary Value Problems. AMS, Providence, Rhode Island, 1979. · Zbl 0414.34025
[7] RACHŮNKOVÁ I.: The first kind periodic solutions of differential equations of the second order. Math. Slovaca, 39 (1989), 407-415. · Zbl 0753.34028
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