Hopf Bifurcation for a Class of Partial Differential Equation with Delay

MR2126324 Azevedo, Katia A. G. and Ladeira, Luiz A. C. Katia A. G. AZEVEDO and Luiz A. C. LADEIRA Hopf Bifurcation for a Class of Partial Differential Equation with Delay Funkcialaj Ekvacioj. Serio Internacia 47 2004 395--422 http://fe.math.kobe-u.ac.jp/FE/FullPapers/47-3/47_395.pdf http://www.ams.org/mathscinet-getitem?mr=MR2126324 We study a kind of delayed reaction-diffusion equation with Dirichlet boundary condition. We show the existence of a sequence of values $\{\tau_{k_n}\}_{n=0,1,2,\ldots}$ of the parameter $\tau$ such that a Hopf bifurcation occurs when the delay passes through each value $\{\tau_{k_n}\}$. The main techniques used here are some results on nonlinear eigenvalue problems, the analysis of the characteristic equation of the linearized problem, the Liapunov-Schmidt method and the implicit function theorem. Partial functional-differential equation, Distributed delay, Periodic solution, Hopf bifurcation, Population dynamics. 35R10, 35B32, 35K55, 92D25. 47-395 2004 Hopf Bifurcation for a Class of Partial Differential Equation with Delay AZEVEDO, Katia A. G. and LADEIRA, Luiz A. C. Katia A. G. AZEVEDO and Luiz A. C. LADEIRA 1 Santos, J. S.; Bená, M. A., Hopf Bifurcation For a Delay Reaction-Diffusion Equation With Negative Feedback, to appear on Revista Brasileira de Matemática e Estatística MR2143724 2 Santos, J. S.; Bená, M. A., The Delay Effect on Diffusion-Reaction Equations, to appear on Applicable Analisys MR2072310

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