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.


34B15 Nonlinear boundary value problems for ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
Full Text: DOI


[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.