On Periodic Solutions of Nonlinear Functional Differential Equations

Abstract Sufficient conditions are established for the existence and uniqueness of an ω-periodic solution of the functional differential equation where f is a continuous operator acting from the space of n-dimensional ω-periodic continuous vector functions into the space of n-dimensional ω-periodic and summable on [0, ω] vector functions.

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On periodic solutions to autonomous retarded functional differential equations

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700018219 ◽

1990 ◽

Vol 41 (3) ◽

pp. 347-354

Author(s):

Zhanyuan Hou

Keyword(s):

Differential Equation ◽

Periodic Solution ◽

Periodic Solutions ◽

Functional Differential Equations ◽

Sufficient Conditions ◽

Sufficient Condition ◽

Retarded Functional Differential Equations ◽

Retarded Functional Differential Equation ◽

Functional Differential ◽

Necessary And Sufficient

Under the assumption that Ca = C([−r, 0], Sn−1(a)) is positively invariant for a > 0, two necessary and sufficient conditions are obtained for an autonomous retarded functional differential equation to have a non-trivial periodic solution in Ca. Moreover, a feasible sufficient condition is given, which is better for n = 2 than that given by Dos Reis and Baroni.

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Asymptotic Behavior for Nonoscillatory Solutions of Second Order Nonlinear Functional Differential Equation

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.616-618.2137 ◽

2012 ◽

Vol 616-618 ◽

pp. 2137-2141

Author(s):

Zhi Min Luo ◽

Bei Fei Chen

Keyword(s):

Differential Equation ◽

Asymptotic Behavior ◽

Differential Equations ◽

Functional Differential Equation ◽

Functional Differential Equations ◽

Sufficient Conditions ◽

Nonoscillatory Solutions ◽

Nonlinear Functional ◽

Nonlinear Functional Differential Equation ◽

Functional Differential

This paper studied the asymptotic behavior of a class of nonlinear functional differential equations by using the Bellman-Bihari inequality. We obtain results which extend and complement those in references. The results indicate that all non-oscillatory continuable solutions of equation are asymptotic to at+b as under some sufficient conditions, where a,b are real constants. An example is provided to illustrate the application of the results.

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On the existence of periodic solutions for autonomous retarded functional differential equations on R2

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500026342 ◽

1986 ◽

Vol 102 (3-4) ◽

pp. 259-262 ◽

Cited By ~ 1

Author(s):

J. G. Dos Reis ◽

R. L. S. Baroni

Keyword(s):

Differential Equation ◽

Periodic Solution ◽

Differential Equations ◽

Periodic Solutions ◽

Functional Differential Equations ◽

Continuous Functions ◽

Retarded Functional Differential Equations ◽

Existence Of Periodic Solutions ◽

Functional Differential

SynopsisLet Ca be the set of all the continuous functions from the interval [−r, 0] on the sphere of radius a, on the plane. We prove, under certains conditions, that a retarded autonomous differential equation that leaves Ca invariant has a non-constant periodic solution.

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Asymptotic behavior of nonoscillatory solutions of a higher order functional differential equation

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700007462 ◽

1981 ◽

Vol 24 (1) ◽

pp. 85-92 ◽

Cited By ~ 1

Author(s):

Hiroshi Onose

Keyword(s):

Differential Equation ◽

Asymptotic Behavior ◽

Differential Equations ◽

Functional Differential Equations ◽

Sufficient Conditions ◽

Nonoscillatory Solutions ◽

Nonlinear Functional ◽

Functional Differential ◽

Approach Zero ◽

Image Position

The asymptotic behavior of nonoscillatory solutions of nth order nonlinear functional differential equationsis investigated. Sufficient conditions are provided which ensure that all nonoscillatory solutions approach zero as t → ∞.

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Properties of Third-Order Nonlinear Functional Differential Equations with Mixed Arguments

Abstract and Applied Analysis ◽

10.1155/2011/857860 ◽

2011 ◽

Vol 2011 ◽

pp. 1-15 ◽

Cited By ~ 13

Author(s):

B. Baculíková

Keyword(s):

Differential Equation ◽

Functional Differential Equations ◽

Sufficient Conditions ◽

Comparison Theorems ◽

Third Order ◽

Nonlinear Functional ◽

The Third ◽

Property B ◽

Functional Differential ◽

Mixed Arguments

The aim of this paper is to offer sufficient conditions for property (B) and/or the oscillation of the third-order nonlinear functional differential equation with mixed arguments . Both cases and are considered. We deduce properties of the studied equations via new comparison theorems. The results obtained essentially improve and complement earlier ones.

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Existence of Subharmonic Periodic Solutions to a Class of Second-Order Non-Autonomous Neutral Functional Differential Equations

Abstract and Applied Analysis ◽

10.1155/2012/404928 ◽

2012 ◽

Vol 2012 ◽

pp. 1-26 ◽

Cited By ~ 1

Author(s):

Xiao-Bao Shu ◽

Yongzeng Lai ◽

Fei Xu

Keyword(s):

Differential Equation ◽

Periodic Solutions ◽

Lower Semicontinuous ◽

Functional Differential Equations ◽

Conjugate Function ◽

Point Theory ◽

Second Order ◽

Neutral Functional Differential Equations ◽

Nonlinear Functional ◽

Functional Differential

By introducing subdifferentiability of lower semicontinuous convex functionφ(x(t),x(t−τ))and its conjugate function, as well as critical point theory and operator equation theory, we obtain the existence of multiple subharmonic periodic solutions to the following second-order nonlinear nonautonomous neutral nonlinear functional differential equationx″(t)+x″(t−2τ)+f(t,x(t),x(t−τ),x(t−2τ))=0,x(0)=0.

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Nonoscillation theorems for functional differential equations of arbitrary order

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171284000259 ◽

1984 ◽

Vol 7 (2) ◽

pp. 249-256 ◽

Cited By ~ 1

Author(s):

John R. Graef ◽

Myron K. Grammatikopoulos ◽

Yuichi Kitamura ◽

Takasi Kusano ◽

Hiroshi Onose ◽

...

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Functional Differential Equation ◽

Arbitrary Order ◽

Functional Differential Equations ◽

Sufficient Conditions ◽

Oscillatory Solutions ◽

Nonlinear Functional ◽

Functional Differential ◽

Nonoscillation Theorem

The authors give sufficient conditions for all oscillatory solutions of a sublinear forced higher order nonlinear functional differential equation to converge to zero. They then prove a nonoscillation theorem for such equations. A few intermediate results are also obtained.

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Existence and Uniqueness of Periodic Solutions of Mixed Monotone Functional Differential Equations

Abstract and Applied Analysis ◽

10.1155/2009/162891 ◽

2009 ◽

Vol 2009 ◽

pp. 1-13 ◽

Cited By ~ 4

Author(s):

Shugui Kang ◽

Sui Sun Cheng

Keyword(s):

Differential Equation ◽

Periodic Solutions ◽

Operator Theory ◽

Existence And Uniqueness ◽

Functional Differential Equations ◽

Existence Results ◽

Mixed Monotone Operator ◽

First Order ◽

Functional Differential ◽

Monotone Operator Theory

This paper deals with the existence and uniqueness of periodic solutions for the first-order functional differential equation with periodic coefficients and delays. We choose the mixed monotone operator theory to approach our problem because such methods, besides providing the usual existence results, may also sometimes provide uniqueness as well as additional numerical schemes for the computation of solutions.

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Almost Periodic Solutions of Monotone Second-Order Differential Equations

Advanced Nonlinear Studies ◽

10.1515/ans-2011-0304 ◽

2011 ◽

Vol 11 (3) ◽

Author(s):

Moez Ayachi ◽

Joël Blot ◽

Philippe Cieutat

Keyword(s):

Differential Equation ◽

Hilbert Space ◽

Periodic Solution ◽

Periodic Solutions ◽

Existence And Uniqueness ◽

Sufficient Conditions ◽

Almost Periodic Solution ◽

Almost Periodic Solutions ◽

Almost Periodic ◽

Second Order Differential Equations

AbstractWe give sufficient conditions for the existence of almost periodic solutions of the secondorder differential equationu′′(t) = f (u(t)) + e(t)on a Hilbert space H, where the vector field f : H → H is monotone, continuous and the forcing term e : ℝ → H is almost periodic. Notably, we state a result of existence and uniqueness of the Besicovitch almost periodic solution, then we approximate this solution by a sequence of Bohr almost periodic solutions.

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