Mean-periodic operational calculi

Ivan Dimovski; Krystyna Skórnik

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Periodic solutions for $n$ -th order delay differential equations with damping terms

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By using the coincidence degree theory of Mawhin, we study the existence of periodic solutions for $n$ th order delay differential equations with damping terms $x^{(n)} (t) = \sum_{i = 1}^{s} b_{i} {[x^{(i)} (t)]}^{2 k - 1} + f (x (t - τ (t))) + p (t)$ . Some new results on the existence of periodic solutions of the investigated equation are obtained.

Existence and positivity of solutions for a nonlinear periodic differential equation

Ernest Yankson (2012)

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We study the existence and positivity of solutions of a highly nonlinear periodic differential equation. In the process we convert the differential equation into an equivalent integral equation after which appropriate mappings are constructed. We then employ a modification of Krasnoselskii’s fixed point theorem introduced by T. A. Burton ([4], Theorem 3) to show the existence and positivity of solutions of the equation.