| 概要 | "An intriguing feature of the global study of nonlinear functional differential equations (FDEs) is that progress in understanding even the simplest-looking FDEs has been slow and has involved a combination of careful analysis of the equation and heavy machinery from functional analysis and algebraic topology. A partial list of tools which have been employed includes fixed point theory and the fixed point index, global bifurcation theorems, a global Hopf bifurcation theorem, the Fuller index, ideas related to the Conley index, and equivariant degree theory. Nevertheless, even for the so-called Wright's equation y'(t)=-a y(t-1)[1+y(t)], (a: real parameter) which has been an object of serious study for more than forty-five years, many questions remain open." Roger Nussbaum, 2002.
In this talk, we introduce a rigorous numerical method to compute global smooth branches of periodic solutions of delay equations. In particular, we use this technique to partially answer a nearly fifty years old conjecture that states that Wright's equation has a unique slowly oscillating periodic solution, for every parameter value a>pi/2.
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