Existence of periodic solutions for first-order totally nonlinear neutral differential equations with variable delay

Abdelouaheb Ardjouni; Ahcène Djoudi

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Fixed points and differential equations with asymptotically constant or periodic solutions.

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On existence of positive periodic solutions of a kind of Rayleigh equation with a deviating argument

Yinggao Zhou, Min Wu (2010)

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The existence of positive periodic solutions for a kind of Rayleigh equation with a deviating argument $x^{''} (t) + f (x^{'} (t)) + g (t, x (t - τ (t))) = p (t)$ is studied. Using the coincidence degree theory, some sufficient conditions on the existence of positive periodic solutions are obtained.

On the existence of one-signed periodic solutions of some differential equations of second order

Jan Ligęza (2006)

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We study the existence of one-signed periodic solutions of the equations $\begin{matrix} x^{''} (t) - a^{2} (t) x (t) + μ f (t, x (t), x^{'} (t)) = 0, & x^{''} (t) + a^{2} (t) x (t) = μ f (t, x (t), x^{'} (t)), \end{matrix}$ where $μ > 0$ , $a : (- \infty, + \infty) \to (0, \infty)$ 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.

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