Ordinary differential equations which yield periodic solutions of differential delay equations
James L. Kaplan,James A. Yorke +1 more
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This article is published in Journal of Mathematical Analysis and Applications.The article was published on 1974-11-01 and is currently open access. It has received 178 citations till now. The article focuses on the topics: Stochastic partial differential equation & Differential algebraic equation.read more
Citations
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Journal ArticleDOI
Existence of periodic and subharmonic solutions for second-order superlinear difference equations
Zhiming Guo,Jianshe Yu +1 more
TL;DR: In this article, the existence and multiplicity results of periodic and subharmonic solutions for difference equations were studied by critical point theory, and some new results were obtained for the above problems when f(t, z) has superlinear growth at zero and at infinity in z.
BookDOI
Delay Differential Equations and Applications
TL;DR: In this paper, Hale et al. present a theory of linear delay differential equations in infinite dimensional spaces, based on Hopf Bifurcation and normal forms for delay differentials.
Book
Bifurcation Theory of Functional Differential Equations
Shangjiang Guo,Jianhong Wu +1 more
TL;DR: The Dynamic Bifurcation Theory of Functional Differential Equations (DBDE) as discussed by the authors is an extension of FDEs with center manifold reduction and Lyapunov-Schmidt reduction.
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The Fuller index and global Hopf bifurcation
Shui-Nee Chow,John Mallet-Paret +1 more
TL;DR: Using an index for periodic solutions of an autonomous equation defined by Fuller, this paper proved the existence of periodic solutions for delay equations with several rationally related delays, for example, x (t) = −α[ax(t − 1) + bx(t− 2)]g(x( t)), with a and b non-negative and α greater than some computable quantity ξ(a, b) calculated from the linearized equation.
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A global bifurcation theorem with applications to functional differential equations
TL;DR: In this article, the existence of a closed, connected unbounded subset S 0 of the set {( x, α ): F ( x, α ) = x and x ≠ 0} for a certain class of nonlinear operators F such that F (0, α) = 0 for all α in an interval of real numbers is established.
References
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Book
Partial Differential Equations
TL;DR: In this paper, the authors present a theory for linear PDEs: Sobolev spaces Second-order elliptic equations Linear evolution equations, Hamilton-Jacobi equations and systems of conservation laws.
Journal ArticleDOI
Periodic solutions of some nonlinear autonomous functional differential equations
TL;DR: In this paper, some fixed point theorems were developed and applied to the question of existence of nontrivial periodic solutions of nonlinear, autonomous functional differential equations, and the standard results of G. S. Jones and R. B. Grafton can be obtained by their methods, and they prove periodicity results for some equations, for instance a neutral functional differential equation.
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Existence of periodic solutions of autonomous functional differential equations
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Periodic solutions of some nonlinear, autonomous functional differential equations. II
TL;DR: In this paper, some fixed point theorems were developed and applied to the question of existence of nontrivial periodic solutions of nonlinear, autonomous functional differential equations, and the standard results of G. S. Jones and R. B. Grafton can be obtained by their methods, and they prove periodicity results for some equations, for instance a neutral functional differential equation.