Displaying similar documents to “Remarks on Krasnoselskii bifurcation theorem”

On bifurcation intervals for nonlinear eigenvalue problems

Jolanta Przybycin (1999)

Annales Polonici Mathematici

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We give a sufficient condition for [μ-M, μ+M] × {0} to be a bifurcation interval of the equation u = L(λu + F(u)), where L is a linear symmetric operator in a Hilbert space, μ ∈ r(L) is of odd multiplicity, and F is a nonlinear operator. This abstract result provides an elementary proof of the existence of bifurcation intervals for some eigenvalue problems with nondifferentiable nonlinearities. All the results obtained may be easily transferred to the case of bifurcation from infinity. ...