A notion of boundedness for hyperfunctions and Massera type theorems

Yasunori Okada

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Displaying similar documents to “A notion of boundedness for hyperfunctions and Massera type theorems”

Periodic solutions of nth order delay Rayleigh equations

Gen-Qiang Wang, Sui Sun Cheng (2002)

Annales Polonici Mathematici

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A priori bounds are established for periodic solutions of an nth order Rayleigh equation with delay. From these bounds, existence theorems for periodic solutions are established by means of Mawhin's continuation theorem.

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.

Positive periodic solutions in neutral nonlinear differential equations.

Raffoul, Y. (2007)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

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Existence and uniqueness of periodic solutions for a kind of nonlinear nth order differential equations with delays

Weiwen Shao, Fuxing Zhang, Ya Li (2008)

Annales Polonici Mathematici

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By applying the continuation theorem of coincidence degree theory, we establish new results on the existence and uniqueness of 2π-periodic solutions for a class of nonlinear nth order differential equations with delays.

Singularly perturbed set of periodic functional-differential equations arising in optimal control theory

Glizer, Valery Y.

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We consider the singularly perturbed set of periodic functional-differential matrix Riccati equations, associated with a periodic linear-quadratic optimal control problem for a singularly perturbed delay system. The delay is small of order of a small positive multiplier for a part of the derivatives in the system. A zero-order asymptotic solution to this set of Riccati equations is constructed and justified.

Resolvent of nonautonomous linear delay functional differential equations

Joël Blot, Mamadou I. Koné (2015)

Nonautonomous Dynamical Systems

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The aim of this paper is to give a complete proof of the formula for the resolvent of a nonautonomous linear delay functional differential equations given in the book of Hale and Verduyn Lunel [9] under the assumption alone of the continuity of the right-hand side with respect to the time,when the notion of solution is a differentiable function at each point, which satisfies the equation at each point, and when the initial value is a continuous function.

On the Existence and Uniqueness of Periodic Solutions of Differential Delay Equations.

Sergio Invernizzi, Fabio Zanolin (1978)

Mathematische Zeitschrift

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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 $\frac{d}{d t} D u_{t} (t) = p (t) - a (t) u (t) - a (t) g (u (t - τ (t))) - h (u (t), u (t - τ (t))) .$ 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...

Existence of periodic solution for first order nonlinear neutral delay equations.

Wang, Genqiang, Yan, Jurang (2001)

Journal of Applied Mathematics and Stochastic Analysis

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Lower bounds and positivity conditions for Green's functions to second order differential-delay equations.

Gil', M.I. (2009)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

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Periodic solutions of a differential delay equation of Rayleigh type

S. Invernizzi, F. Zanolin (1979)

Rendiconti del Seminario Matematico della Università di Padova

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Global existence results for second order neutral functional differential equation with state-dependent delay

Mouffak Benchohra, Imene Medjadj (2016)

Commentationes Mathematicae Universitatis Carolinae

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Our aim in this work is to provide sufficient conditions for the existence of global solutions of second order neutral functional differential equation with state-dependent delay. We use the semigroup theory and Schauder's fixed point theorem.