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On the existence of two solutions of the periodic problem for the ordinary second-order differential equation. (English) Zbl 0808.34023
The author considers the differential equation \(u'' + f(u)u' + g(t,u,u') = s\), \(t \in I\), where \(s \in\mathbb R\) is a parameter, \(I = [a,b] \subset\mathbb R\), \(f \in C(R)\) and \(g \in C(I \times\mathbb R^ 2)\), under periodic conditions \(u(a) = u(b)\), \(u'(a) = u'(b)\). Using a certain relation between strict upper and lower solutions and the coincidence topological degree some theorems on the number of solutions are proved. Some examples are given.
Reviewer: M. Goebel (Halle)

MSC:
34B15 Nonlinear boundary value problems for ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
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[1] Fabry, C.; Mawhin, J.; Nkashama, M.N., A multiplicity result for periodic solutions of forced nonlinear second order ordinary differential equations, Bull. London math. soc., 18, 173-180, (1986) · Zbl 0586.34038
[2] Rachu̇unková, I., The first kind periodic solutions of differential equations of the second order, Math. slovaca, 39, 407-415, (1989)
[3] Rachu̇unková, I., Multiplicity results for four-point boundary value problems, Nonlinear analysis, 18, 497-505, (1992)
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