## On the periodic boundary-value problem for systems of second-order nonlinear ordinary differential equations.(English)Zbl 0824.34027

The author considers the periodic boundary value problem $$x''= f(t, x, x')$$, $$x(a)= x(b)$$, $$x'(a)= x'(b)$$. Conditions for the existence and uniqueness of solutions for the above boundary value problem are obtained. The techniques involve among others modified function theory, differential inequalities and Nagumo type conditions.

### MSC:

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

### Keywords:

periodic boundary value problem; existence; uniqueness
Full Text:

### References:

 [1] I. T. Kiguradze, Some singular boundary-value problems for ordinary differential equations (Russian)Tbilisi University Press, Tbilisi, 1975. [2] L. H. Erbe and P. K. Palamides, Boundary-value problems for secondorder differential equations.J. Math. Anal. Appl. 127 (1987), 80–92. · Zbl 0635.34017 [3] G. D. Gaprindashvili, On Solvability of the Dirichlet boundary-value problem for systems of ordinary nonlinear differential equations with singularities. (Russian)Differential’nye Uravneniya 27 (1991), No. 9, 1521–1525. · Zbl 0745.34016 [4] G. D. Gaprindashvili, On certain boundary value problems for systems of second-order nonlinear ordinary differential equations. (Russian)Proc. I. Vekua Inst. Appl. Math. Tbilis. St. Univ. 31 (1988), 23–52. · Zbl 0735.34019 [5] M. Nagumo, Über die Differentialgleichungy”=f(x,y,y’).Proc. Phys.-Math. Soc. Japan 19 (1937), 861–866. · JFM 63.1021.04 [6] Ph. Hartman, Ordinary differential equations.John Wiley & Sons, New York, 1964. · Zbl 0119.07302
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.