Bifurcation at multiple eigenvalues and stability of bifurcating solutions Academic Article uri icon

abstract

  • If K is a bounded linear operator from the real Banach space U into the real Banach space V and f{hook}:URV has the value zero at (0, 0), the existence and linear stability of the equilibrium solutions of the dynamical system K du dt = f{hook}(u, ) which are close to the origin in UR are studied. It is assumed that f{hook}u(0, 0): U V is a Freholm operator of index zero. The only restriction on the dimension of the null space of f{hook}u(0, 0) and the order of vanishing, at (0, 0), of f{hook} restricted to the null space of Df{hook}(0,0):URV, is that they both be finite positive integers. The main result gives conditions under which the equation, which determines the equilibrium solutions in a neighborhood of the origin, also determines the stability of these equilibrium solutions. 1984.

published proceedings

  • Journal of Functional Analysis

author list (cited authors)

  • Taliaferro, S. D.

citation count

  • 6

complete list of authors

  • Taliaferro, Steven D

publication date

  • February 1984