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Upper and lower solutions for periodic problems. (English) Zbl 1090.34552

Summary: Upper and lower solutions method, topological degree and Miranda fixed-point theorem are applied to obtain the existence of at least one periodic solution for second-order and first-order nonlinear differential systems.

MSC:

34C25 Periodic solutions to ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
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References:

[1] Leela, S., Monotone method for second order periodic boundary value problems, Nonlinear Anal., 7, 349-355 (1983) · Zbl 0524.34023
[2] Lakshmikantham, V.; Leela, S., Remarks on first and second order periodic boundary value problems, Nonlinear Anal., 8, 281-287 (1984) · Zbl 0532.34029
[3] Habets, P.; Zanolin, F., Upper and lower solutions for a generalized Emden-Fowler equation, J. Math. Anal. Appl., 181, 684-700 (1994) · Zbl 0801.34029
[4] Rachunkova, I., Upper and lower solutions and topological degree, J. Math. Anal. Appl., 234, 311-327 (1999) · Zbl 1086.34017
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