Geodesic
On the existence of one-signed periodic solutions of some differential equations of second order
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 45 (2006) no. 1, pp. 119-134.

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We study the existence of one-signed periodic solutions of the equations \begin{align} x^{\prime \prime } (t) - a^2(t) x(t) + \mu f(t, x(t), x^{\prime }(t)) = 0, x^{\prime \prime }(t) + a^2(t) x(t) = \mu f(t, x(t), x^{\prime }(t)), \end{align} where $ \mu > 0$, $a: (-\infty , +\infty ) \rightarrow (0, \infty ) $ is continuous and 1-periodic, $f$ is a continuous and 1-periodic in the first variable and may take values of different signs. The Krasnosielski fixed point theorem on cone is used.
Classification : 34B10, 34B15, 34B18, 34C25, 34G20, 34K10, 47N20
Keywords: positive solutions; boundary value problems; cone; fixed point theorem 
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Ligęza, Jan. On the existence of one-signed periodic solutions of some differential equations of second order. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 45 (2006) no. 1, pp. 119-134. http://geodesic.mathdoc.fr/item/AUPO_2006__45_1_a11/