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Existence of solutions to first-order periodic boundary value problems. (English) Zbl 1109.34016

The paper deals with the question on the existence of a solution to the periodic problem for nonlinear differential systems. The assumptions of the main result (namely Theorem 2.2) guarantee a priori estimates on possible solutions to a certain family of boundary value problems, which yields the existence of a solution of the problem considered.

MSC:

34B15 Nonlinear boundary value problems for ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
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[1] Abd-Ellateef, K.; Ahmed, R.; Drici, Z., Generalized quasilinearization for systems of nonlinear differential equations with periodic boundary conditions, Dyn. contin. discrete impuls. syst. ser. A math. anal., 12, 1, 77-85, (2005) · Zbl 1092.34508
[2] Chen, J., On the existence of solutions for PBVP for first-order differential equations, Acta math. sci. ser. A chin. ed., 23, 129-134, (2003) · Zbl 1040.34019
[3] Ding, W.; Mi, J.; Han, M., Periodic boundary value problems for the first-order impulsive functional differential equations, Appl. math. comput., 165, 2, 433-446, (2005) · Zbl 1081.34081
[4] Franco, D.; Nieto, J.J.; O’Regan, D., Anti-periodic boundary value problem for nonlinear first-order differential equations, Math. inequal. appl., 6, 477-485, (2003) · Zbl 1097.34015
[5] Hakl, R.; Lomtatidze, A.; Šremr, J., On nonnegative solutions of a periodic type boundary value problem for first-order scalar functional differential equations, Funct. differ. equ., 11, 3-4, 363-394, (2004) · Zbl 1078.34045
[6] He, Z.; He, X., Periodic boundary value problems for first-order impulsive integro-differential equations of mixed type, J. math. anal. appl., 296, 1, 8-20, (2004) · Zbl 1057.45002
[7] Lloyd, N.G., Degree theory, (1978), Cambridge Univ. Press Cambridge · Zbl 0367.47001
[8] Obersnel, F.; Omari, P., Old and new results for first-order periodic ODEs with uniqueness: a comprehensive study by lower and upper solutions, Adv. nonlinear stud., 4, 323-376, (2004) · Zbl 1072.34041
[9] Peng, P., Positive solutions for first-order periodic boundary value problem, Appl. math. comput., 158, 345-351, (2004) · Zbl 1082.34510
[10] C.C. Tisdell, On first-order boundary value problems, Preprint
[11] Wan, Z.; Chen, Y.; Chen, J., Remarks on the periodic boundary value problems for first-order differential equations, Comput. math. appl., 37, 8, 49-55, (1999) · Zbl 0936.34013
[12] Yakovlev, M.N., Solvability of a periodic boundary value problem for a system of first-order ordinary differential equations with \((\beta, \gamma, \delta)\)-comparison pairs, J. math. sci. (N.Y.), 101, 3365-3371, (2000)
[13] Yang, X., Upper and lower solutions for periodic problems, Appl. math. comput., 137, 2-3, 413-422, (2003) · Zbl 1090.34552
[14] Zhang, F.; Ma, Z., Nonlinear boundary value problems for first-order differential equations with piecewise constant arguments, Ann. differential equations, 19, 431-438, (2003) · Zbl 1057.34071
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