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Conference Proceeding

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Many applications give rise to separable parameterized equations of the form A(y,µ)z + b(y, µ) = 0, where y Rn, z RN and the parameter µ R; here A(y,µ) is an (N + n) × N matrix and b(y, µ) RN +n. Under the assumption that A(y, µ) has full rank we showed in [21] that bifurcation points can be located by solving a reduced equation of the form f (y, µ) = 0. In this paper we extend that method to the case that A(y, µ) has rank deficiency one at the bifurcation point. At such a point the solution curve (y, µ, z) branches into infinitely many additional solutions,which form a straight line. A numerical method for reducing the problem to a smaller space and locating such a bifurcation point is given. Applications to equilibrium solutions of nonlinear ordinary equations and solutions of discretized partial differential equations are provided.

Publication Title

Electronic Journal of Differential Equations



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Published by the Department of Mathematics, Texas State University


Eighth Mississippi State - UAB Conference on Differential Equations and Computational Simulations

This is an open access journal.

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Mathematics Commons