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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
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References:

[1] I. T. Kiguradze, Some singular boundary-value problems for ordinary differential equations (Russian)Tbilisi University Press, Tbilisi, 1975.
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