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We study the existence and stability of periodic solutions of a differential equation that models the planar oscillations of a satellite in an elliptic orbit around its center of mass. The proof is based on a suitable version of Poincaré-Birkhoff theorem and the third order approximation method.
In this paper, we study the existence, multiplicity and stability of positive periodic solutions of relativistic singular differential equations. The proof of the existence and multiplicity is based on the continuation theorem of coincidence degree theory, and the proof of stability is based on a known connection between the index of a periodic solution and its stability.
In the setting of mean-square exponential dichotomies, we study the existence and uniqueness of mean-square almost automorphic solutions of non-autonomous linear and nonlinear stochastic differential equations.
We study the prevalence of stable periodic solutions of the forced relativistic pendulum equation for external force which guarantees the existence of periodic solutions. We prove the results for a general planar system.
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