On bifurcation intervals for nonlinear eigenvalue problems
Volume 71 / 1999
Annales Polonici Mathematici 71 (1999), 39-46
DOI: 10.4064/ap-71-1-39-46
Abstract
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.
