Colloquium, Department of Mathematics and Statistics
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Duan Chen

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Wednesday, Jan 16, 11:00AM-12:00 Noon, Conference room

January 11, 2019 by Duan Chen
Categories: Spring 2022
Inbo Sim, University of Ulsan, South Korea
Title: Symmetry-breaking bifurcation for the one-dimensional H\'{e}non and Moore-Nehari differential equations
Abstract: We show the existence of a symmetry-breaking bifurcation point for the one-dimensional H\'{e}non and the  Moore-Nehari differential equation.

 Employing a variant of Rabinowitz’s global bifurcation, we obtain the unbounded connected set (the first of the alternatives about Rabinowitz’s global bifurcation), which emanates from the symmetry-breaking bifurcation point. Moreover, we give an example of a bounded branch connecting two symmetry-breaking bifurcation points (the second of the alternatives about Rabinowitz’s global bifurcation) and show that a bifurcation point for Moore-Nehari equation is explicitly represented as a function of \p\ which is an exponent of nonlinear term.

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