Stability of solutions bifurcating from multiple eigenvalues Academic Article uri icon

abstract

  • Let X and Y be real Banach spaces and G:X × R be a twice continuously differentiate function which is not necessarily linear. Suppose G(u0, α0) = 0 and the dimension of the null space of Gu(u0, α0) is m, where 1 ≤ m < ∞. Usually, S = {(u, α):G(u, α) = 0}, in a neighborhood of (u0, α0), consists of a finite number of curves emanating from (u0, α0). We will determine the stability of points, (u, α), in S (i.e., the maximum of the real parts of the spectrum of Gu(u, α) for each (u, α) ∈ S) using a general perturbation theorem of Kato. Our results contain as a special case the stability theorems of Crandall and Rabinowitz for the case m = 1. We will also tie our stability theorems together with some bifurcation results of Decker and Keller. Finally we apply our results to systems of reaction diffusion equations. © 1981.

published proceedings

  • Journal of Functional Analysis

author list (cited authors)

  • Taliaferro, S. D

citation count

  • 12

complete list of authors

  • Taliaferro, Steven D

publication date

  • October 1981