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Wu, Jianhong

Global continua of periodic solutions to some difference-differential equations of neutral type. (English) Zbl 0778.34054

Tôhoku Math. J., II. Ser. 45, No. 1, 67-88 (1993).
The author shows some theorems which are used to study the existence of periodic solutions of neutral equations. Among other things, he presents extensions to neutral equations of the following results: a) local Hopf bifurcation theorem of Krasnosel’skij type [M. A. Krasnosel’skij, Topological methods in the Theory of Nonlinear Integral Equations, Oxford (1964; Zbl 0111.303)]; b) global bifurcation theorems of J. C. Alexander and J. A. Yorke [Am. J. Math. 100, 263-292 (1978; Zbl 0386.34040)] or P. H. Rabinowitz [J. Funct. Anal. 7, 487-513 (1971; Zbl 0212.165)]; c) a well known result for retarded equations by S.-N. Chow and J. Mallet-Paret [J. Differ. Equations 29, 66-88 (1978; Zbl 0369.34020)]. A specific example arising from the lossless transmission lines is studied. Moreover, a good information concerning the applications of neutral equations is given. The paper finishes stating some unanswered interesting questions.
Reviewer: A.Cañada (Granada)

Cited in 12 Documents

MSC:

34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
34K40 Neutral functional-differential equations
34C25 Periodic solutions to ordinary differential equations
34C23 Bifurcation theory for ordinary differential equations

Keywords:

periodic solutions; neutral equations; local Hopf bifurcation theorem of Krasnosel’skij type; global bifurcation theorems; retarded equations; example; lossless transmission lines

Citations:

Zbl 0111.303; Zbl 0386.34040; Zbl 0212.165; Zbl 0369.34020
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\textit{J. Wu}, Tôhoku Math. J. (2) 45, No. 1, 67--88 (1993; Zbl 0778.34054)
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References:

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