Displaying similar documents to “Periodic solutions of nth order delay Rayleigh equations”

Periodic solutions for some delay differential equations appearing in models of power systems

Bingwen Liu, Lihong Huang (2005)

Annales Polonici Mathematici

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The authors use coincidence degree theory to establish some new results on the existence of T-periodic solutions for the delay differential equation x''(t) + a₁x'(t) + a₂(xⁿ(t))' + a₃x(t)+ a₄x(t-τ) + a₅xⁿ(t) + a₆xⁿ(t-τ) = f(t), which appears in a model of a power system. These results are of practical significance.

A notion of boundedness for hyperfunctions and Massera type theorems

Yasunori Okada (2012)

Banach Center Publications

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For some classes of periodic linear ordinary differential equations and functional equations, it is known that the existence of a bounded solution in the future implies the existence of a periodic solution. In order to think on such phenomena for hyperfunction solutions to linear functional equations, we introduced a notion of bounded hyperfunctions, and translated the problems into the problems on analytic solutions to some equations in complex domains. In this article,...

Existence and Stability of Periodic Solutions for Nonlinear Neutral Differential Equations with Variable Delay Using Fixed Point Technique

Mouataz Billah MESMOULI, Abdelouaheb Ardjouni, Ahcene Djoudi (2015)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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Our paper deals with the following nonlinear neutral differential equation with variable delay d d t D u t ( t ) = p ( t ) - a ( t ) u ( t ) - a ( t ) g ( u ( t - τ ( t ) ) ) - h ( u ( t ) , u ( t - τ ( t ) ) ) . By using Krasnoselskii’s fixed point theorem we obtain the existence of periodic solution and by contraction mapping principle we obtain the uniqueness. A sufficient condition is established for the positivity of the above equation. Stability results of this equation are analyzed. Our results extend and complement some results obtained in the work [Yuan, Y., Guo, Z.: On the existence and...